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Space Optical Clocks (SOC)

(2007-2009)

ESTEC Contract Nr 20579/07/NL/VJ

Midterm Report September 2008

Project board representatives/ Project team members: S. Schiller, Heinrich-Heine-Universität Düsseldorf (HHUD-I)(coordinator) A. Görlitz, Heinrich-Heine-Universität Düsseldorf (HHUD-II) G. Tino, Universita di Firenze/LENS(UNIFI/LENS) U. Sterr, Physikalisch-Technische Bundesanstalt Braunschweig (PTB) P. Lemonde, SYRTE Paris C. Salomon, Ecole Normale Superieure (ENS)

The work of HHUD-I, HHUD-II, PTB is also funded by DLR Contract 50 QT 0701

„Entwicklung optischer Atomuhren auf der Basis ultrakalter Atome für Weltraumanwendungen“

Contract Officer: Dr. E. Bachem

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Contributors to this report Team SYRTE P. Lemonde Group Leader J. Lodewyck post-doc P.G. Westergaard PhD student A. Lecallier PhD student. Team PTB U. Sterr staff scientist, Group Leader C. Lisdat staff scientist T. Legero staff scientist F. Riehle staff scientist, Head of PTB’s Optics Department S. R. J. V. Winfred PhD student Team HHUD-I A. Nevsky Group leader U. Bressel PhD student I. Ernsting PhD student M. Okhapkin Guest researcher A. Wicht Ass. Prof. Prof. S. Schiller Head Team HHUD-II F. Baumer PhD student N. Nemitz PhD student C. Abou Jaoudeh PhD student C. Bruni Master student Prof. A. Görlitz Group leader Team LENS Prof. G. M. Tino head Prof. M. Prevedelli associate professor G. Ferrari researcher M. de Angelis researcher N. Poli researcher F. Sorrentino Post-Doc M. Schioppo Ph. D. student. Team ENS Prof. Ch. Salomon Group Leader The team members thank their respective technical staff for essential support.

Figures on title page: top: design of a compact cold atom apparatus (LENS); bottom: strontium atoms trapped in an optical lattice (thin horizontal line) and a cloud of strontium atoms falling freely inside the vacuum chamber (PTB).

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Contents Page

A.0 Abstract 5

A.1 Introduction and motivation 7 - 8

A.2 The neutral atom lattice optical clock 9 - 12

A.3 Deliverables 13 - 14

A.4 Main results achieved by the teams until midterm 15 - 16

A.5 Milestones 17 - 18

A.6 Deliverables 19

A.7 Initiatives taken by the team to consolidate and enlarge

the non-space industry 19

A.8 International cooperation 21

A.9 Funding from national space agencies and from other sources 23

A.10 List of inventory items 23

A.11 List of publications 25 - 27

A.12 List of presentations 29 - 32

B Description of work packages 33 - 96

C Planned work 97 - 99

D References 101 - 103

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A.0 Abstract

The aim of the three-year project is to implement several optical lattice clock laboratory demonstrator systems using Strontium and Ytterbium as atomic systems, to characterize and compare them, to test and validate different operational procedures and specifications required for operation in space. Subcomponents of the clock demonstrator with the added specification of transportability and using techniques that are suitable for later space use, such as all-solid-state lasers, low power consumption, and small volume, will be developed and validated. The outcome of these activities will be a demonstration of spectroscopy of the clock transition in cold strontium atoms with a transportable apparatus. At the end of the 3-year project, the specifications for a space clock will be finalized. Status: At midterm, several components and systems were developed, including, lasers, reference cavities, optical fiber links, cold atom chambers. Main achievements to date are clock lasers with relative frequency instability of 1×10-15 on short term, the observation of the clock transitions in four systems, including achievement of the resolved motional sideband regime, with spectral resolution up to 1.5×1013. One system has been well-characterized with respect to systematic shifts, with a fractional frequency inaccuracy 2.6×10-15 and a fractional instability of 1.5×10-15 at 3000 s integration time. A number of components and subsystems are under development with the aim of compact size and low power consumption. Left: Ultra-cold strontium atoms trapped in a laser beam; right: design of a compact cold atom apparatus (length: 52 cm).

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A.1 Introduction and motivation Clocks are essential tools in modern society. Clocks operate in computers, data networks, are ubiquitous in scientific applications and are even operated in satellites, especially in navigation systems such as GPS, GLONASS and the European Galileo system. Time, or more precisely, time intervals, is the most precisely measurable quantity. Since the speed of electromagnetic waves in vacuum is invariable, distance measurements can be performed by wave propagation timing measurements. It also follows that ultimately, the precision of distance measurements is limited by the available precision in time measurements. In the international system of units, the unit of time, the second, is based on an atomic hyperfine transition in neutral cesium (Cs) atoms. Laboratory clocks using cold Cs atoms have today an accuracy of a few parts in 1016, i.e. such clocks exhibit errors equivalent to less than a second over 100 million years. Although this accuracy is already very high, outstanding advances in laser and quantum technology have opened the way to the realization of significantly more accurate and more stable clocks. It is generally expected that clocks operating in the optical domain of the electromagnetic spectrum rather than in the microwave domain (as cesium clocks do) will bring at least two orders of magnitude improvement. This is because in optical clocks the periodic electromagnetic wave beats 1015 times per second instead of 1010 as in microwave clocks. Therefore, one can detect (and also correct) much faster a minute change of the period. A hundredfold improvement in stability compared to the best microwave clocks, to a level of 1 part in 1017, is expected within the next few years (our consortium is a key player in this development), and probably even more over the next decade. In addition, several, but not all, perturbing effects of the energy levels of the atoms are smaller in relative terms for optical transitions compared to microwave transitions, and a large gain is therefore also expected in the accuracy. Optical atomic clocks use optical transitions in laser cooled neutral atoms or ions as quantum frequency reference (QFR) (see Figure A.1). The invention of the femtosecond frequency comb has made it possible to precisely count frequencies in the optical domain, and to transform them into the radiofrequency domain, and by now optical frequency counters are well-developed systems, also available commercially. The challenges for optical atomic clocks are the establishment of techniques for reliable and simple preparation of suitable QFRs, the control of systematic effects to a high degree of accuracy, and the development of the required components, in particular ultrastable laser sources at the frequencies corresponding to the clock transitions. There is a growing effort worldwide on these issues. More than 10 groups are already working in this field. In parallel, approaches are being studied towards transportable optical atomic clocks, including such suitable for space operation, which is the aim of the SOC project. Optical clocks with the above accuracy will have a strong impact both in fundamental physics (e. g. for measurements of the space-time variation of fundamental constants), for various aspects of general relativity, in applied physics and for geophysics. Some of these applications can be best pursued with space clock instruments and proposals for fundamental physics missions using optical clocks were made in the 2007 Cosmic Vision call for proposals. It is an important insight that eventually only in space will it be possible to take full advantage of the performance of optical clocks, since on earth the clock frequency is influenced by the earth’s gravitational potential at the location of the clock, contributing with an uncertainty on the order of one part in 1017 if distant clocks are compared. Therefore, in the future, applications requiring the highest accuracy will require placing optical clocks on satellites, e.g. in geostationary orbits or Lagrange points; they will become “master clocks in space”.

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Figure A.1. Prinicple of an optical atomic clock. A laser, the local oscillator, interrogates an ensemble of ultracold atoms, the quantum frequency reference (QFR). In the case of a lattice optical clock (shown) the atoms are at µKelvin temperature and trapped by laser waves. The interrogation by the local oscillator results in a signal proportional to the absorption of the laser light (frequency ν), which is maximum for a light frequency ν0 corresponding to the center of the atomic resonance. With a feedback control, the laser frequency ν is continuously kept tuned on the atomic resonance frequency. The resulting ultra-stable optical frequency can be converted to an equally stable radio-frequency by means of a femtosecond laser frequency comb. Picture credit: PTB.

Oszillator

ν0

Atome, Moleküle oder Ionen

Detektor

Regelungs-elektronik

νν0

νν0

S

Absorptions- signal

FehlersignaldSdν

Detector

absorber single ion

Laser

Femto- second frequency comb

Cold atoms

Absorption

Error signal

Feedback control

electronics

Optical frequency ~ 400 000 GHz

Radio - frequency signal, 200 MHz

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A.2 The neutral atom lattice optical clock In this section we give a brief overview of the elements and operation of a lattice optical clock. It serves to better understand the workpackage descriptions. A.2.1 Basic principle A neutral atom clock is an alternative is based on a large number of neutral atoms (on the order of 105) confined in an optical lattice trap within an ultra high vacuum (UHV) chamber, and laser cooled to few microKelvin temperature. The optical lattice trap is produced by a laser (Fig. A.2). Due to the low temperature of the atoms and the appropriate choice of the wavelength of the trapping laser, both the first order Doppler and the AC Stark effects will not affect the accuracy of the frequency reference. Under these conditions, the narrow-linewidth 5 1S0 → 5 3P0 clock transition in strontium at 698 nm (or the 6 1S0 → 6 3P0 clock transition at 578 nm in ytterbium) can be interrogated with high fidelity by a spectrally narrow and stable clock laser source. The clock laser is a semiconductor laser diode frequency stabilized against a reference optical cavity.

The clock transition spectral profile is observed by stepping the clock laser frequency by means of an acousto-optic frequency shifter (AOM), and recording the fraction of the atoms excited in the higher clock state as a function of this frequency. The clock laser is stabilised to the clock transition by repeatedly stepping back and forward between the half-intensity points on the clock frequency profile, monitoring the excitation imbalance between these points and servo-correcting any detected imbalance to zero by means of feedback to the AOM.

Figure A.2 Counter-propagating laser beams form interference patterns that lead to an array of intensity wells, spaced by a fraction of a micrometer (optical lattice). Atoms in this lattice are interrogated by a clock laser.

A diagram of the simplified energy level scheme for the two atom species investigated in

this project, showing the relevant cooling, auxiliary and clock transitions is given in Figure A.3. All wavelengths associated with the colored arrows are provided by compact diode laser system, operated in fundamental or frequency doubled mode.

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Figure A.3: Electronic level schemes of 87Sr (left) and Yb (right), showing the relevant cooling, possible auxiliary (repumper) and clock transitions. The optical lattice trapping laser is shown in grey on the left. For Yb, the lattice laser wavelength is 759 nm. A.2.2 Detailed description To be specific, we consider a clock based on Sr atoms, and consider an architecture that could be made compact for space use. Note that in this project the studies will not always follow this architecture for reasons of flexibility. The space-type optical clock will comprise the following components (see Figure A.5) • a magneto-optic trap for loading and cooling about 105 87Sr atoms within an ultra-high vacuum chamber pumped by a small ion pump and non-evaporable getter pump. The atoms are initially evaporated in an oven cartridge under vacuum, subsequently they are collimated towards the trapping region and slowed by radiation pressure, then they are captured and cooled in the magneto-optic trap (MOT), and finally they are loaded into the standing wave optical dipole trap for excitation of the clock transition. Figure A.4 shows two examples of MOTs. After exposure to the clock light the population remaining in the ground state is measured by obtaining the fluorescence signal in presence of the blue (cooling) light. While the operation of the MOT requires a magnetic quadrupole field produced by electromagnets, the clock interrogation is sensitive to stray magnetic fields and needs homogeneous constant fields on the order of 0.1 mT or less. Then additional electromagnets allow the compensation of the magnetic field on the atoms, and a mu-metal shield surrounding the vacuum system suppresses the external field changes. • a laser source delivering 461 nm light for slowing the atomic beam and first (or pre-) cooling on the 1S0 - 1P1 transition. This sub-module includes an extended cavity diode laser (ECDL) at 922 nm which is amplified through a semiconductor tapered amplifier and then frequency doubled to 461 nm. The MOPA set-up insures 1 W power in the infrared and 461 nm light is produced by second-harmonic generation (SHG). This generation will be implemented in a double-pass geometry without the need of an enhancement resonator. More than 100 mW are blue radiation is obtained to enable operation of the clock.

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Figure A.4: Magneto-optic traps with a samples of fluorescing cold Sr atoms (left, LENS) and cold Yb atoms (right, HHUD-II), illuminated by the (pre-) cooling laser light at 461 nm (left) and 397 nm (right). • a laser for the second cooling stage at 689 nm on the 1S0 - 3P1 transition. This module includes an extended cavity laser diode locked to a medium finesse cavity in order to reach a spectral linewidth on the order of 1 kHz. Before reaching the atoms, this radiation is amplified into an injection- locked slave diode laser delivering up to 30 mW, and it passes through a acusto-optic modulator for the FM and AM modulation required for the operation of the second stage cooling. • the optical bench also houses the lasers for optical pumping from the metastable clock state, and optical dipole trapping at the magic wavelength. The first repumper, resonant on the 3P0 - 3S1 transition, is an extended cavity diode laser at 679 nm delivering 1 mW. At PTB and SYRTE the second repumper is based on the 707 nm 3P2 – 3S1 transition. Another option (pursued at LENS) is a laser resonant on the 3P2 - 3D2 transition at 497 nm, implemented as an extended cavity diode laser or a distributed feedback (DFB) diode laser at 994 nm, delivering 30 mW, and subsequently frequency doubled with a nonlinear-optical crystal in a double-pass geometry without the need of an enhancement resonator. Finally, the dipole trapping laser is an extended cavity diode laser at 813 nm, amplified to 400 mW using a semiconductor tapered amplifier. • a high NA lens imaging and photodiode detection system to record the 461 nm atomic fluorescence after exposure to the 698 nm clock laser with varying frequency detuning. This provides the quantum frequency reference and allows to steer the ULE cavity-stabilised clock laser. • a fibre system to deliver the various cooling, auxiliary and clock laser waves from the laser sources to the trap, making use of achromatic doublets where necessary at the fibre-free space interface for launching into the trap • a monitoring and control processor, which provides the cooling and clock laser pulses, magnetic field and detection sequencing to observe and lock to the atom clock transition frequency. The processor also monitors frequency and amplitude data necessary to determine normal laser and atomic source operational conditions and initiate resetting and recovery algorithms where necessary, and laser unit failure. • a redundancy level of at least 2 units for cooling, clock, repumper and trapping lasers, plus similar for frequency doubling crystals. All redundancy units for each wavelength to be fibre

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multiplexed as standard, allowing redundant unit activation on determination of prior unit failure mode.

Figure A.5: Simplified schematic of the neutral atom clock. Grey arrows originate from the power distribution unit. DPE: data processing unit.

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A.3 List of deliverables

WP

deliverable

due date

WP 1.1 Sr clock

physics package optimization I

Report: - Evaluation and optimization of lattice

configurations Report: Performance of second-generation sub-systems

month +24

month +36 WP 1.2 Sr clock

physics package optimization II

Report: Sensitivity evaluation to environmental disturbances Report: - Evaluation of lattice configurations, interrogation and detection schemes.

month +18

month +30

WP 1.3 Strontium pre-cooling laser

Report: Pre-cooling laser package

month+24

WP 1.4 Transportable cold Strontium source

Report: experimental package Transportable Sr source apparatus

month+24

WP 1.4.1 Cold atom source

integration

Report: experimental package for first cooling and trapping Sr.

month+30

WP 1.4.2 Sr clock integration

Report: first test on Sr clock transition interrogation month+36

WP 1.5: Sr clock laser

Report: optimized cavity designs Clock laser package

month + 12

month + 24 WP 1.6: Sr clock

characterization

Report: Evaluation of performance of two Sr clocks

month + 36

WP 2.1 Cold Ytterbium

Source

Report: - Evaluation of pre-cooling schemes for fermionic and bosonic Yb using diode lasers Report: - Full characterization of a dedicated source of ultracold Yb for an optical lattice clock

month +18

month +22

WP 2.2: Ytterbium trap-laser

and optical lattice setup

Report: - Design of an optical lattice at the magic wavelength for Yb Report: - Full characterization of Yb optical lattice at the magic wavelength

month + 18

month + 24

WP 2.3 Yb clock laser

Report: Yb clock laser design and performance evaluation

month +23

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WP 2.4

Ytterbium clock component

integration and characterization

Report: - Characterization of the optical clock transition in Yb in a magneto-optical trap. Report: - Characterization and systematic study of an optical lattice clock for bosonic and fermionic Yb - Evaluation of prospects for further improvements and implementation in space mission.

month + 24

month +36

WP 3: Clock laser comparison

Report: Clock-laser comparison results month +24

WP 4: Synthesis

Report: Evaluation of results, design for a space optical clock, roadmap

month +36

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A.4 Main results Team SYRTE

• Sr clock evaluation by comparison with Cs atomic fountains, reaching an accuracy of 2 10-15 and a frequency stability of 10-15 (WP 1.6).

• Construction of a second generation Sr vacuum system, implementing the deflection of the atomic beam before capture by the blue MOT (WP1.1).

• Design, realization and tests of a new vibration insensitive ultra-stable cavity. Vibration sensitivity is below 10-11/(m/s2) along all three axis and frequency stability between 1 and 2 10-15 at 1s (WP 1.6).

• Demonstration of a fiber based frequency transfer with frequency noise <10-18 at 10000 s over a distance of 172 km (WP 1.6).

• Construction of a semiconductor laser based second generation lattice (WP 1.1) Team PTB

• Sr clock physics package optimization II (WP 1.2) - Modelling of trap loading dynamics - Characterization of trap parameters - Investigations of density dependent shifts and broadenings in a 88Sr lattice clock.

• Sr clock laser development (WP 1.5) - Setup of 698 nm clock laser and vibration insensitive cavity - Linewidth measurement by comparison to PTB’s ultrastable 657 nm laser - Phase-lock of the laser to ultra-stable laser via a femtosecond optical comb generator.

Team HHUD-I

• Development and characterization of a novel semiconductor laser system at 1156 nm (WP 2.3)

• Prestabilization of clock laser to a cavity (WP 2.3) • Thermal characterization and stabilization of a ULE reference cavity (WP 2.3) • Development of a stabilized 350 m optical fiber link joining two laboratories (WP 2.4) • Observation and first frequency measurement of clock transition in 171Yb with the

semiconductor laser (WP 2.4, together with HHUD-II) Team HHUD-II • Experimental realization of a precooling MOT (at 399nm) with Yb using an all-diode laser

based system (WP 2.1.) • Experimental realization and characterization of a scheme for direct loading of Yb into a

postcooling MOT (at 556nm) (WP 2.1.) • Loading of Yb into an optical trap (WP 2.1.) • Setup and initial characterization of a compact dedicated apparatus for the Yb clock (WP

2.1.) • Development and setup of a high power grating-stabilized diode laser for the magic-

wavelength optical lattice for Yb. (WP 2.2.) • Development, building and optical characterization of a robust setup for a magic-wavelength

3D-optical lattice with bosonic Yb (WP 2.2.) • Observation of the optical clock transition in fermionic 171Yb in a MOT (together with

HHUD-I, WP 2.4.)

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Team LENS

• realization of a compact, long-term stable source of cooling light for Sr, with output power P > 300 mW (WP1.3)

• design of a compact complete cold Sr atom apparatus (WP 1.4) • Tests performed on the Sr ovens (WP1.4) • Development of fiber system (achromatic fiber splitter/fiber launcher) for improved

stability, compatible with second stage cooling of Sr isotopes (WP1.4) • Lattice spectroscopy of clock transition in 88Sr isotope • Actively stabilized fiber system between clock laser lab and cold atom lab

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A.5 Milestones SYRTE: Reduction of systematic effects in Sr to a level below 1.10-15 (+ 18 months) Corresponding achievement: Evaluation was performed at a level of 2 x 10-15

Achievement of instability of Sr clock below 1.10-15 (+ 18 months) Corresponding achievement: A stability of 1.10-15 was achieved. Reduction of systematic effects in Sr to a level below 1.10-16 (+ 36 months) In planning Achievement of instability of Sr clock below 1.10-16 (+ 36 months) In planning PTB: Determination of optimized cavity designs (+18 months): Technical Note completed. Cavity has been built and tested, but showed excessive sensitivity to vibrations, most likely because of mechanical contact of cavity to vacuum chamber. Currently a second spacer is manufactured and an additional vacuum system is set up. When this is operational, the first vacuum chamber will be opened to examine the position of the spacer. Transportable Sr clock laser with 1 Hz linewidth and short-term instability (RAV) 1 Hz, characterized (+ 24 months) Laser is set up and operating, linewidth still around ~ 30 Hz due to problems of cavity Spectroscopy of clock transition with a transportable cold Sr apparatus at mK temperature (+36 months) Planning in progress Determination of a clock design for a transportable Sr clock capable of operating at inaccuracy below 1·10-16 level (+ 36 months) Technical note discussing the systematic effects has been completed. It will be updated when the current measurements of collisional effects are completed. Düsseldorf I: Yb clock laser with 1 Hz linewidth and short-term instability (RAV) < 1 Hz, characterized (+ 24 months) ULE cavity system developed; prestabilization of laser implemented (1 kHz linewidth, 200 Hz RAV) Düsseldorf II: Evaluation of pre-cooling schemes for bosonic and fermionic Yb (+ 18 month) This milestone has been reached. For the realization of an Yb optical clock we have decided on a two-stage cooling scheme for all isotopes (bosonic and fermionic). The result of the evaluation is reported on in a technical note. Ultracold Yb source, characterized (+24 month)

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The level of completion for this milestone is 75%. We have fully characterized the already existing stationary source for ultracold Yb which is shared with other experimental studies. Currently the performance of the new compact Yb source is being evaluated. Due to the setup of this new dedicated apparatus, which will eventually allow for a much better clock performance than the previous apparatus and is potentially transportable, the completion of this milestone is estimated for (+ 27 month). Operation of Yb clock with inaccuracy below 1x10-14 /Operation of Yb clock with instability below 1x10-15 (+ 36 months) (together with Düsseldorf I) The level of completion for this milestone is 20%. Initial spectroscopic studies in a 171Yb MOT operating on the 1S0 → 3P1 have already been performed. LENS: Transportable laser for Sr first-stage cooling (+ 24 months) Completed

Apparatus for transportable cold Sr source (+24 months) Design completed, compact breadboard for MOT frequencies assembled at 75% level

Transportable cold Sr source, characterized (+30 months) The level of completion for this milestone is 50%. Transportable laser has been tested, achieving a stable Sr MOT. Similar test will be performed after the completion of the transportable vacuum setup. Spectroscopy of clock transition with a transportable cold Sr apparatus at mK temperature (+36 months, together with PTB) In planning ALL (WP4): Determination of a clock design for a transportable Sr clock capable of operating at inaccuracy below 1.10-16 level (+ 36 months) In planning

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A.6 Deliverables SYRTE: No deliverables are due by midterm PTB: “Cavity Design Guidelines”, revised version delivered August 21, 2008

“Systematics in a Sr Lattice Clock”, revised version delivered September 3, 2008 HHUD-I: No deliverables are due by midterm HHUD-II: Evaluation of pre-cooling schemes for fermionic and bosonic Yb using diode

lasers (subm. Dec. 2008)

Design of an optical lattice at the magic wavelength for Yb (subm. Jan 2009) LENS: No deliverables are due by midterm A.7 Initiatives taken by the team to consolidate and enlarge the non-space industry partnership in the Project, including through proposals submitted to the relevant EC programmes, the details of the outcome of these initiatives and the further planning of the team on that subject The project “optical clocks for a future definition of the second” has been proposed to EU via the EURAMET e.V. call for European metrology in September 2007. This projects involves two of the partners of the present consortium (PTB, SYRTE), as well as the British, Italian and Finnish National metrology institutes (NPL, INRIM, MIKES respectively). It is coordinated by SYRTE. The project has been accepted and formally started on April 1st 2008 for a 3 year duration. The goal of the project is to study Sr confined in an optical lattice as a possible candidate for a future redefinition of the second and aims at reducing various contribution to the uncertainty of strontium Lattice clocks. Funding obtained: LNE-SYRTE 360 k€, PTB 582 k€ over three years, starting from April 1, 2008. Prof. Görlitz has coordinated the proposal QUAFRO (Quantum Frequency References in the Optical Domain - Towards improved Optical Clocks) within the EuroQUASAR call of the EuroCores programme run by ESF. The proposing team combined all members of SOC with additional partners in Germany, Austria, Denmark and Great Britain. After a positive preevalutaion the coordinator was invited to submit a full proposal which was recommended for funding by the panel of reviewers. Due to the inability of two of the national funding agencies to give enough financial support to the proposal the whole proposal could finally not be funded according to the rules of ESF.

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A.8 International cooperation and team performance enhancement The clock laser development undertaken by HHUD-I was based on a cooperation with a high-tech-start-up company, Innolume. The company is run by Russian scientists, but located in Germany. The project consortium is of the opinion that a strong coordination between the ongoing activities in this project and activities of the TEC department at ESTEC or ESOC should be implemented. It is to be emphasized that members of the consortium have previously participated in two ESA studies: - Study On The Feasibility And Applications Of Optical Clocks As Frequency And Time References In ESA Deep Space Stations ESA contract 19838/06/F/VS (Contractor: Kayser Italia) Participation: HHUD-I, HHUD-II, LENS, SYRTE - Optical frequency synthesizer for space-borne optical frequency metrology ESTEC/Contract No 19595/06/NL/PM (Contractor: National Physical Laboratory) Participation: HHUD-I These studies have looked in depth into medium-term and far-term applications of optical clocks as related to space (see following section for a brief overview), they have compared in detail different implementations and have laid out specifications of optical clocks for particular uses, such as for ESA ground stations. A development plan for a breadboard system and a roadmap for the realization of a compact optical frequency reference have been defined. It is clear that the developments within this ELIPS project are very valuable for the topics studied above. The consortium emphasizes the need for avoidance of competition or duplication of activities within ESA, such as activities to be undertaken within the Cosmic Vision Program. Indeed, in the assessment of the first round of calls, the space sciences committee has expressed the need for the development of technology for fundamental physics missions and optical clocks were mentioned in particular. The consortium has therefore expressed his position in a letter (dated Sept. 5, 2008) to the contractor (National Physical Laboratory) of a TEC study producing a development plan for optical clocks.

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A.9 Funding from national space agencies and from other sources A contract between CNES and SYRTE for the development of optical lattice clocks has been signed in the frame CNES RT studies for 2007 and 2008. It amounts to 124.2 k€. A new proposal was submitted for 2009 and 2010. The two teams of Heinrich-Heine-University Düsseldorf and the PTB team have received complementary funding by the German Space Agency DLR. The project is entitled “Entwicklung optischer Atomuhren auf der Basis ultrakalter Atome für Weltraumanwendungen”, Number 50QT0701, 1.6.2007 – 30.12.2009, amount: 289.293 €, covering manpower, equipment, and consumables The combined HHUD-I and II amount obtained is 193.293 €, which is precisely the amount stated in the contract document to be obtained from the national space organisation. Team HHUD-I had stated an amount 23 k€ from other sources; this was covered through overhead funds from an EU project. The amount obtained by PTB is 96 k€, which is actually more than the sum of 51 + 35 k€ stated in the contract. A.10 List inventory of items (> 3000 €) purchased till midterm. SYRTE: none PTB: none HHUD-I Optical fiber, Fibercore, € 4464,91 Fiber installation (material + assembly), Elektrobau Kegel, € 6287,85 HHUD-II Optical isolator for 1112 nm, Thorlabs, € 3336.94 LENS: none

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A.11 List of publications SYRTE X. Baillard, M. Fouché, R. Le Targat, P.G. Westergaard, A. Lecallier, F. Chapelet, M. Abgrall, G.D. Rovera, P. Laurent, P. Rosenbusch, S. Bize, G. Santarelli, A. Clairon, P. Lemonde, G. Grosche, B. Lipphardt and H. Schnatz, . “An optical lattice clock with spin-polarized 87Sr atoms”, Eur. Phys. J. D, 48, 11 (2008). Abstract: We present a new evaluation of an 87Sr optical lattice clock using spin polarized atoms. The frequency of the 1S0 → 3P0 clock transition is found to be 429 228 004 229 873.6 Hz with a fractional uncertainty of 2.6 × 10−15, a value that is comparable to the frequency difference between the various primary standards throughout the world. This measurement is in excellent agreement with a previous one of similar accuracy [Phys. Rev. Lett. 98, 083002 (2007)]. Xavier Baillard, Mathilde Fouché, Rodolphe Le Targat, Philip G. Westergaard, Arnaud Lecallier, Yann Le Coq, Giovanni D. Rovera, Sebastien Bize and Pierre Lemonde “Accuracy evaluation of an optical lattice clock with bosonic atoms”, Opt. Lett. 32, 1812 (2007) Abstract: We report what we believe to be the first accuracy evaluation of an optical lattice clock based on the 1S0→3P0 transition of an alkaline earth boson, namely, 88Sr atoms. This transition has been enabled by using a static coupling magnetic field. The clock frequency is determined to be 429 228 066 418 009 (32) Hz. The isotopic shift between 87Sr and 88Sr is 62 188 135 Hz with fractional uncertainty 5 10−7. We discuss the necessary conditions to reach a clock accuracy of 10−17 or less by using this scheme. S. Blatt, A. D. Ludlow, G. K. Campbell, J.W. Thomsen, T. Zelevinsky, M. M. Boyd, and J. Ye, X. Baillard, M. Fouché, R. Le Targat, A. Brusch, and P. Lemonde, M. Takamoto, F.-L. Hong, and H. Katori, V.V. Flambaum, “New Limits on Coupling of Fundamental Constants to Gravity Using 87Sr Optical Lattice Clocks”, Phys. Rev. Lett. 100, 140801 (2008) Abstract: The 1S0-3P0 clock transition frequency νSr in neutral 87Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the 1 10-15 level makes νSr the best agreed-upon optical atomic frequency. We combine periodic variations in the 87Sr clock frequency with 199Hg+ and H-maser data to test local position invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant α, electron-proton mass ratio µ, and light quark mass. Furthermore, after 199Hg+, 171Yb+, and H, we add 87Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of α and µ. PTB T. Legero, Ch. Lisdat, J.S.R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, U. Sterr, Interrogation laser for a strontium lattice clock, Accepted for publication in IEEE Trans. Instrum. Meas. (2008) - The authors gratefully acknowledge the support by the Deutsche Forschungsgemeinschaft under SFB 407, by ESA, DLR, and the Centre for Quantum Engineering and Space-Time Research (QUEST). Abstract: We report on the setup and characterization of a 698 nm master-slave diode laser system to probe the 1S0 – 3P0 clock transition of strontium atoms confined in a one-dimensional optical lattice. A linewidth in the order of around 100 Hz of the laser system has been measured

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with respect to an ultrastable 657 nm diode laser with 1 Hz linewidth using a femtosecond fiber comb as transfer oscillator. The laser has been used to measure the magnetically induced 1S0 – 3P0 clock transition in 88Sr where a linewidth of 165 Hz has been observed. The transfer oscillator method provides a virtual beat signal between the two diode lasers that has been used to phase lock the 698 nm laser to the 1 Hz linewidth laser at 657 nm, transferring its stability to the 698 nm laser system. HHUD-I A. Yu. Nevsky, U. Bressel, I. Ernsting, Ch. Eisele, M. Okhapkin, S. Schiller, A. Gubenko, D. Livshits, S. Mikhrin, I. Krestnikov, A. Kovsh, “A narrow-linewidth external cavity quantum dot laser for high-resolution spectroscopy in the near-infrared and yellow spectral ranges”, Appl. Phys. B 92, 501-507 (2008)

Abstract: We demonstrate a diode laser system which is suitable for high-resolution spectroscopy in the 1.2 µm and yellow spectral ranges. It is based on a two-facet quantum dot chip in a Littrow-type external cavity configuration. The laser is tunable in the range 1125 -1280 nm, with an output power of more than 200 mW, and exhibits a free-running linewidth of 200 kHz. Amplitude and frequency noise were characterized, including the dependence of frequency noise on the cavity length. Frequency stabilization to a high-finesse reference cavity is demonstrated, whereby the linewidth was reduced to approx. 30 kHz. Using a femtosecond frequency comb, the residual frequency instability was determined and found to be below 300 Hz on the time scales 1 - 300 s. Yellow light (> 3 mW) at 578 nm was generated by frequency doubling in an enhancement cavity containing a PPLN crystal. The source has potential application for precision spectroscopy of ultra-cold Yb atoms and cold molecular hydrogen ions. HHUD-II N. Nemitz, F. Baumer, F. Münchow, S. Tassy, A. Görlitz, “Production of ultracold heteronuclear YbRb* molecules by photoassociation”, arXiv:0807.0852 - work partially funded by the German Research Foundation (DFG) under SPP1116 (while this publication is scientifically related to a research project on ultracold molecules, the development of the directly loaded postcooling MOT has been shared with this project) Abstract: We have produced ultracold heteronuclear YbRb¤ molecules in a combined magneto-optical trap by photoassociation. The formation of electronically excited molecules close to the dissociation limit was observed by trap loss spectroscopy in mixtures of 87Rb with 174Yb and 176Yb. The molecules could be prepared in a series of vibrational levels with resolved rotational structure, allowing for an experimental determination of the long-range potential in the electronically excited state.

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LENS N. Poli, R. E. Drullinger, G. Ferrari, M. Prevedelli, F. Sorrentino, M. G. Tarallo, and G. M. Tino, “Prospect for a compact strontium optical clock”, Proc. of SPIE 6673, 66730F (2007) Abstract: We report on our progress toward the realization of a compact optical frequency standard referenced to strontium intercombination lines. Our current setup allows the production of ultracold Sr atoms in hundreds of ms. For high resolution spectroscopy of 1S0-3P0 doubly forbidden transition we have prepared a 698 nm clock laser stabilized on high finesse symmetrically suspended cavity and a high power 813 nm light source for the optical lattice trap at the magic wavelength. All the laser source employed are based on semiconductor device. A new Sr trapping and cooling experimental setup is also under development. This opens the way to the realization of compact, reliable and eventually transportable optical frequency standards.

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A.12 Presentations at conferences and institutions SYRTE P.G. WESTERGAARD, A. LECALLIER, J. LODEWYCK AND P. LEMONDE, “Optical lattice clocks with Sr atoms”, 7th Symposium on Frequency Standards and Metrology, Pacific Grove, California, USA, 2008. A. LECALLIER, PG. WESTERGAARD, X. BAILLARD, J. LODEWYCK AND P. LEMONDE, “Towards the Comparison of Independent Strontium Optical Lattice Clocks », 22nd European Frequency and Time Forum, Toulouse, France, 2008. A. LECALLIER, P.G. WESTERGAARD, X. BAILLARD, J. LODEWYCK AND P. LEMONDE, “Towards the Comparison of Independent Strontium Optical Lattice Clocks”, 2008 IEEE International Frequency Control Symposium, Honolulu, Hawaii, USA, 2008. X. BAILLARD, M. FOUCHÉ, R. LE TARGAT, P.G. WESTERGAARD, A. LECALLIER, P. LEMONDE ET AL., « An Optical Lattice Clock with Fermionic and Bosonic Sr Atoms », CLEO-Pacific Rim, Seoul, Korea, 2007 X. BAILLARD, M. FOUCHÉ, R. LE TARGAT, P.G. WESTERGAARD, A. LECALLIER, P. LEMONDE ET AL., « 87Sr optical lattice clock using spin-polarized atoms», ECAMP IX, Heraklion, Greece, 2007 J. LODEWYCK, A. LECALLIER, P. WESTERGAARD, X. BAILLARD AND P. LEMONDE, “Towards the Comparison of Independent Strontium Optical Lattice Clocks”, Second ESA International Workshop on Optical Atomic Clocks, ESA-ESRIN, Frascati, Italy, 2007. X. BAILLARD, M. FOUCHÉ , R. LE TARGAT, P.G. WESTERGAARD, A. LECALLIER, P. LEMONDE ET AL., « An Optical Lattice Clock with Spin-polarized 87Sr Atoms », TimeNav'07-Joint EFTF IEEE-FCS, Geneva, Switzerland, 2007

X. BAILLARD, M. FOUCHÉ , R. LE TARGAT, P.G. WESTERGAARD, A. LECALLIER, P. LEMONDE ET AL., « Using spin-polarized atoms for an optical lattice clock with strontium», ICONO/LAT, Minsk, Belarus, 2007

P. LEMONDE, "Optical clocks with cold atoms” .Workshop on Quantum Engineering based on Atoms and Photons, Hannover, Germany (2007).

X. BAILLARD, M. FOUCHE , R. LE TARGAT, P.G. WESTERGAARD, A. LECALLIER, P. LEMONDE ET AL., « Horloges à réseau optique à atomes de Strontium. » Optique Grenoble 2007- COLOQ'10, Grenoble, France (2007).

P. LEMONDE P., « Des horloges atomiques pour LISA ? », Journées LISA-France, Annecy, France (2007).

X. BAILLARD, M. FOUCHE , R. LE TARGAT, P.G. WESTERGAARD, A. LECALLIER, P. LEMONDE ET AL., « Horloges à réseau optique à atomes de Strontium. » Congrès Général de la SFP, Grenoble, France (2007).

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PTB T. Legero, Ch. Lisdat, J.S.R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, Clock laser system for a strontium lattice clock, Talk, Conference on Precision Electromagnetic Measurements (CPEM), Boulder, USA, June 10, 2008. T.E.Mehlstäubler, Ch. Lisdat, J.S.R. Vellore Winfred, T. Legero, F. Riehle, U. Sterr, H. Schnatz, G. Grosche, B. Lipphardt, B. Stein, I. Sherstov, Ch. Tamm. E. Peik, Optical clocks and frequency standards – present research at PTB, poster, BIPM Metrology Summer School, Paris, 30 June - 11 July 2008 T. Legero, J.S.R. Vellore Winfred, Ch. Lisdat, F. Riehle, U. Sterr, Towards an optical lattice clock with bosonic strontium, poster, European Frequency and Time Forum (EFTF), Toulouse, France, 23-25 April 2008 U. Sterr, J.S.R. Vellore Winfred, T. Legero, Ch. Lisdat and F. Riehle, Precision measurements with strontium in optical lattices, poster, Coherence, Squeezing and Entanglement for Precision Measurements with Quantum Gases, Levico Terme (Trento, Italy), 3-5 April 2008 T. Legero, F. Riehle, U. Sterr, Clock laser for an optical lattice clock with strontium, poster, Spring Meeting of the German Physical Society, Darmstadt, Germany, 10.-14. March 2008 J.S.R. VelloreWinfred, T. Legero, Ch. Lisdat, F. Riehle, U. Sterr, Ultra-cold strontium atoms in 1-D optical lattice for optical frequency metrology, poster, Spring Meeting of the German Physical Society, Darmstadt, Germany, 10.-14. March 2008 F. Vogt, J.S.R. Vellore Winfred, U. Sterr, Loading dynamics of optical dipole traps for earth alkali atoms, poster, Spring Meeting of the German Physical Society, Darmstadt, Germany, 10.-14. March 2008 T. Legero, J.S.R. Vellore Winfred, Ch. Lisdat, F. Riehle, U. Sterr, Ultracold 88Sr atoms for an optical lattie clock, poster, Quantum-Atom Optics Downunder, Wollongong, Australia, December 3-6, 2007 U. Sterr, Cold neutral atom optical frequency standards at PTB, talk, ESA International Workshop on Optical Atomic Clocks, Frascati, Italy, October 10, 2007 U. Sterr, Atomic frequency standards and their impact on the past, present and future of the second, invited talk, LEOS OFTMAG, IEEE/LEOS Summer Topical Meeting on Optical Frequency/Time Measurement and Generation, Portland OR, USA, July 23, 2007 U. Sterr, T. Nazarova, H. Schnatz, J. S. R. Vellore Winfred, Th. Legero, F. Riehle, Neutral atom optical frequency standards at PTB, poster, 388. WE-Heraeus-Seminar Atomic Clocks and Fundamental Constants ACFC 2007, Bad Honnef, June, 2007 T. Nazarova, Ch. Lisdat, U. Sterr, F. Riehle, Influence of high frequency laser frequency noise on the stability of an atomic clock, poster, European Forum on Time and Frequency, Geneve, May 2007 T. Legero, J. S. R. Vellore Winfred, F. Riehle, U. Sterr, Ultracold 88Sr atoms for an optical lattice clock, poster, European Forum on Time and Frequency, Geneve, May 2007

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H. Schnatz, U. Sterr, Optical Local Oscillators and Combs, talk, Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007 J. S. R. Vellore Winfred, T. Legero, F. Riehle, U. Sterr, Ultracold strontium atoms for optical frequency metrology, poster, Spring meeting of the Deutsche Physikalische Gesellschaft 2007, Düsseldorf, Germany, March 2007 J. S. R. Vellore Winfred, T. Legero, F. Riehle, U. Sterr, Laser cooling of strontium atoms for an optical lattice clock, poster, European-Australian Workshop on Quantum Engineering based on Atoms and Photons, Hannover, Germany, February 2007 U. Sterr, Thomas Legero, Tatiana Nazarova, Christian Lisdat and Fritz Riehle, Lasers for optical clocks with calcium and strontium, talk, European-Australian Workshop on Quantum Engineering based on Atoms and Photons, Hannover, February 2007 HHUD-I S. Schiller, A. Görlitz, U. Sterr, “Entwicklung optischer Atomuhren auf der Basis ultrakalter Atome für Weltraumanwendungen”, presentation given to the review committee on extraterrestrial science, (DLR, Bonn, 8. 6. 2007) S. Schiller et al., "Proposal for a Gravity Explorer Satellite Mission", Conf. on advances in precision tests and experimental gravitation in space" (Firenze, 28 - 30 Sept. 2006) S. Schiller et al., "Proposal for a Gravity Explorer Satellite Mission using Optical Clocks", Workshop on Optical Frequency Combs for Space, (National Physical Laboratory, Teddington, UK, 2nd - 3rd October 2006) S. Schiller, “Optical Frequency Metrology in Space”, Discussion Meeting on Optical Frequency Synthesizers for Space, ESTEC, 13. 10. 2006 and Dec. 2006 S. Schiller, “Gravimetry with Optical Clocks”, Workshop on The Future of Satellite Gravimetry, 12 -13 April 2007, ESTEC S. Schiller, “Gravitational Physics with Optical Clocks in Space”, Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007 S. Schiller, Optical Clocks in Space for Fundamental Physics and Earth gravity studies ‐ the Einstein Gravity Explorer (EGE) mission proposal, 2nd ESA International Workshop on Optical Clocks, ESRIN Frascati, 10.-12.10.2007 S. Schiller, Optical Clocks – Latest Developments and Future Trends, ACES and future GNSS-based Earth observation and navigation, Technische Universität München, 26.-27.5.2008 S. Schiller, Satellitengestützte Tests der Allgemeinen Relativitätstheorie mittels Quantensensoren, Grundlagenforschung im Weltraum, Bayerisches Wirtschaftsministerium, München, 12.-13.6.2008

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HHUD-II F. Baumer, U. Bressel, S. Kroboth, N. Nemitz, A. Nevsky, M. Okhapkin, A. Wicht, S. Schiller, A. Görlitz, Towards an optical clock with neutral Yb, DPG-Frühjahrstagung, Düsseldorf, March 2007.

F. Baumer, U. Bressel, S. Kroboth, N. Nemitz, A. Nevsky, M. Okhapkin, A. Wicht, S. Schiller, A. Görlitz, Towards an optical clock with neutral Yb, Poster, 388th WE-Heraeus-Seminar Atomic Clocks and Fundamental Constants ACFC 2007, Bad Honnef, June, 2007. F. Baumer, N. Nemitz, C. Abou Jaoudeh, A. Görlitz, A new compact apparatus for an ytterbium optical lattice clock, Poster, 2nd ESA International Workshop on Optical Atomic Clocks, Frascati, October 2007 LENS N. Poli, R. E. Drullinger, G. Ferrari, M. Prevedelli, F. Sorrentino, M. G. Tarallo, and G. M. Tino, “Prospect for a compact strontium optical clock”, Proc. of SPIE 6673, 66730F (2007) N. Poli, R. E. Drullinger, M. G. Tarallo, and G. M. Tino, “Strontium optical lattice clock with all semiconductor sources", Proc. of 21st EFTF’07 & IEEE-FCS meeting (Timenav’07), Geneve, (2007)

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B Description of work packages Workpackage 1.1 - Strontium clock physics package optimization (SYRTE) 1.1.1 Tests of optimal lattice parameters for probing the atoms This part of the WP has not been started yet. 1.1.2 Design and construction of a second generation vacuum chamber 1.1.2.1 Beam deflection A second generation vacuum chamber has been constructed. The main modification with respect to the first one is the implementation of the deflection of the Sr atomic beam before atoms are slowed down by the Zeeman slower and captured by the MOT. This deflection is performed by a retro-reflected laser beam red detuned from the 1S0-1P1 blue cooling transition by δ = 1.1γ (γ is the natural linewidth of the transition), acting as an optical molasses. The laser beam is arranged in a retro-reflected V-shaped configuration in the horizontal plane (see figure 1.1.1), and then directed in the vertical direction (orthogonal to the beam propagation) to reduce the atomic transverse velocity spread. The advantages of this new configuration are numerous: -By eliminating thermal atoms in the capture/clock region, this will lead to a longer trap life-time, the elimination of a possible frequency shift due to collisions between hot and cold atoms, and the cancellation of stray fluorescence from the atomic beam. -The cooling of the atoms in the transverse direction associated to the deflection increases the number of atoms trapped in the MOT, thus decreasing the lattice loading time. -The window through which the Zeeman cooling beam enters the vacuum chamber is no longer progressively coated by Sr deposition (this effect presently implies a periodic cleaning of this window on the first vacuum system). These improvements, combined with a new detection scheme which allows keeping (i.e. not loosing) the atoms from one cycle to the next will enable to greatly reduce the required time for preparing the cold atoms, and ultimately optimize the clock frequency stability.

Fig. 1.1.1: Experimental setup for the atomic beam deflection and collimation

We tested the efficiency of the transverse cooling by measuring the number of trapped atoms in the MOT as a function of the collimation laser power. For this experiment, the collimation laser is set orthogonal to the atomic beam propagation, so that the atomic beam is not deflected. This atom number, relative to the number without the collimation laser is plotted in figure 1.1.2. For a collimation laser power of 20 mW, the enhancement reaches a factor of 4, demonstrating the efficiency of the transverse velocity spread reduction.

35

Fig. 1.1.2: Gain in the number of trapped atoms due to the beam deflection as a function of the optical power in the deflecting beam. We then adjusted the V-shaped deflecting beam to obtain a deflection of 30 mrad, sufficient to remove the MOT from the direct view of the oven. In this configuration, with a deflection power of 20 mW we obtained as many atoms in the MOT as in the direct view experiment. Finally, we completed the construction of the second generation vacuum system, implementing all the hardware necessary for a full clock operation (see figure 1.1.3). The clock, however has not been operated yet, due to problems experienced with the lattice laser (see section 1.1.3).

Fig. 1.1.3: Picture of the second generation vacuum system. Front: blue laser system. Back: vacuum chamber: from left to right: ion pump, MOT-Clock region, Zeeman slower, deflection region, Sr oven.

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1.1.2.2 A non-destructive atom detection method We have studied a new detection scheme which should enable to keep the atoms from one cycle of the clock operation to the next. The advantage of keeping atoms is clear: it would enable to minimize the time spent to load the atoms in the lattice (presently the dominant contribution in the various stages of a clock cycle) and hence optimize the clock frequency stability. The latter is determined by the noise degradation due to the conversion of the clock laser frequency noise by the atomic sampling (Dick effect) [Quessada03]. This degradation would be strongly reduced with an optimized cycle. The principle of this new detection scheme is to detect a phase shift induced on a laser beam by the atoms (instead of scattered photons in the traditional detection used so far). The mechanical perturbation of the atoms can be minimized since this phase shift scales as 1/δ (δ is the detuning between the laser and the atomic resonance) while the number of scattered photons (which create the mechanical perturbation and eventually lead to the atom loss) scales as 1/δ2. This method was first demonstrated for Cs atoms in a dipole trap in [Windpassinger2008]. Our modified detection scheme is sketched in Fig. 1.1.4.

Fig. 1.1.4: Sketch of the new detection scheme (see text for explanation). It is based on a heterodyne technique, the idea being to detect an atom-induced phase shift on the beatnote between two probe beams tuned symmetrically around the atomic resonance. These two probe beams are generated by the upper AOM as shown in Fig. 1.1.4, taking both the +1 and -1 orders in a double-pass configuration. The beams are then spatially filtered and two beatnotes are recorded, one reference one taken before interaction with the atoms, one after. We set the power seen by the atoms to less than a microwatt in order to prevent spontaneous emission induced heating. At such low power, a direct measurement of the beatnote would be limited by the noise of the photodiode. We therefore use a relatively high power local oscillator (1 mW) to recover this second beatnote with improved signal to noise ratio. The LO frequency is shifted by 200 MHz from the average probe frequency to lift the degeneracy between both beatnotes and allow proper separation, amplification filtering and recombination of the signals. This setup is highly symmetrical and most sources of technical noise are intrinsically cancelled: laser frequency noise, most beam path fluctuations, RF phase noise etc… The present level of phase noise is shown in Fig. 1.1.5. The white noise limit at high frequency > 200 Hz, is due to the photodiode noise. We expect to reach the quantum limit set by the photon shot noise using a new photodiode. At low frequency (200 Hz and below), residual technical

AOM +1

-1spatial filter

atoms∆φ

461 nm laser

LO~1 mW

Signal <1 µW

Ref ~100 µW

AOM

37

noise sets the present limitation. The present detectivity of the system is about 50 to a 100 atoms for a detection duration of a few ms.

Fig. 1.1.5: Phase noise power spectral density of the non-destructive detection scheme.

1.1.3 Design and construction of a second generation lattice A third important line of activity on WP 1.1 has been the design and construction of a second generation lattice. The goal is to use a fully semiconductor laser system based on an extended cavity laser diode (ECLD) + semiconductor amplifier system. The power consumption, size, weight and cost of such a system being much smaller than the more traditional Ti-Sapphire laser system, it seems particularly suited for a future operation in space. We constructed the ECLD system based on the interference filter design such as used in the PHARAO laser source [Baillard2006]. With about 50 mW of injected power from this ECDL, the power output of a semiconductor amplifier approaches 1W, of which about 50% are coupled to an optical fiber guiding the laser to the clock. Unfortunately, the lifetime of the atoms in the lattice when using this system appears to be very short, and we do not so far keep them long enough for the clock operation. The probable reason for this behaviour is the relative intensity noise of the laser beam which induces a heating of the atoms [Savard1997]. We are presently investigating this issue which may lead to the necessity of a very high bandwidth (tens of MHz) servo-control of the lattice intensity to be able to efficiently reduce the laser intensity noise at twice the atomic oscillation frequency in the lattice (typically 500 kHz in our system). One of the issues is to design a fast and efficient detector for such a servo loop.

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1.1.4 Performed tests: The contract includes 3 series of tests to be performed in the frame of this WP on stationary apparatus: - Dependence of clock performance on lattice parameters. This has essentially not been started. Only the clock frequency has been measured as a function of the lattice depth at a level of 10-15. This is described in Sec.1.6.3. - Performance of the second generation vacuum chamber: The efficiency of the beam deflection is described in Sec.1.1.2. The other aspects of performance will be tested once the full system is operational. - Performance of the second generation lattice: this is described in Sec. 1.1.3.

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Workpackage 1.2 - Sr clock physics package optimization II (PTB) 1.2.1 Modelling trap loading mechanisms For optical clocks based on laser-cooled neutral strontium, both the bosonic isotope 88Sr and the fermionic 87Sr can be used. The physical difference in the application of the two is the process that enables the excitation of the doubly forbidden, ultra-narrow clock transition 3P0 – 1S0 (see Fig. 1.2.1). The natural abundance of 81% favours the application of 88Sr especially in transportable clocks, for which simple techniques to load and prepare the atoms are required. Also the laser cooling and state preparation of 88Sr is simpler than for 87Sr.

461 nm

(5s4d) D12

0

(5s ) S10

2

(5s5p) P11

(5s6s) S31

(5s5p) P3J

1

2Γ = 2.1 · 10 s-18

689 nmΓ = 4.7 · 10 s-14

698 nmΓ = 10 s6 · -1-3

87Sr

Γ = 3.9 · 10 s-13 679 nmΓ = 9 10 s· -16

707 nmΓ = 2.9 10 s· -17

688 nmΓ = 2.5 10 s· -17

Fig. 1.2.1: Simplified level scheme of strontium. Transitions relevant for cooling and spectroscopy are indicated by arrows. Green: clock transition; blue: first stage cooling (pre-) cooling transition; red: second-stage (post-) cooling transition.

For cooling of 88Sr we use a two stage cooling process. In the first cooling stage, 88Sr atoms are captured from a Zeeman-slowed atomic beam and cooled to 2 mK in a magneto-optical trap (MOT) operating on the broad 1S0 – 1P1 transition at 461 nm. This MOT works with a magnetic field gradient of 7.4 mT/cm, and a total laser intensity of 21 mW/cm2. The cooling laser is detuned 54 MHz below the 1S0 – 1P1 transition frequency. After 200 ms 3·107 atoms are trapped in the MOT. For further cooling, a MOT working at the spin-forbidden 1S0 – 3P1 transition at 689 nm is employed. To cover the Doppler shift of the atoms from the first cooling stage and to compensate the limited velocity capture range of the 689 nm MOT the laser spectrum is broadened by modulating the laser frequency at 50 kHz with a peak to peak frequency excursion of 3 MHz. For this operation phase of the 689 nm MOT, a magnetic field gradient of about 0.7 mT/cm, a total intensity of 33 mW/cm2 and a detuning of 1.6 MHz below the 1S0 – 3P1 transition are used. Within a 50 - 70 ms long broadband cooling interval the atoms are cooled down to 15 µK. Finally the frequency modulation is switched off and the cooling laser is operated at a single frequency, detuned 400 kHz below the 1S0 – 3P1 transition. With an intensity of 440 µW/cm2 and a 70 ms long cooling interval this process leads to 8·106 atoms at a temperature of 3 µK (Fig. 1.2.2).

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"Blue" cooling (461 nm)

Broadband cooling (689 nm)

Optical lattice (813 nm)

200 ms

50 ms

70 ms

T ~ 2 mK , N ~ 4 107

T ~15 µK , N ~ 1 107

T ~ 3 µK , N ~ 8 106.

.

.

T ~ 3 µK , N ~ 1 106.

Detection ground state (MOT beams , 461 nm)

Blow-away (461 nm)

Repumper (679 nm, 707 nm)

Detection excited state (MOT beams , 461 nm)

Interrogation laser (698 nm)

20 ms

20 ms

20 ms

20 ms

200 ms

Cooling and trapping sequence

Spectroscopy sequence

0 ms 250 ms 500 ms 750 ms Fig. 1.2.2 Timing of the experiment to load atoms into the optical lattice and detect them after

interrogation with the clock laser.

During the whole cooling process the atomic cloud is superimposed with the horizontally oriented 1D optical lattice operated at 813 nm. At this wavelength the light shifts of the 1S0 and 3P0 states are exactly equal and the clock transition frequency becomes independent of the laser intensity [Katori 2003,Takamoto 2003]. As shown in Fig. 1.2. 3, the 1.1 W output beam of the Ti:sapphire lattice laser is coupled into a polarization maintaining optical fiber and passes through polarization optics before being focused on the center of the atom cloud. The beam is linearly polarized with its polarization oriented perpendicular to gravity. A dichroic mirror is used to retro-reflect the 813 nm laser beam and hence establish the 1D optical lattice. With a beam radius of 30 µm and a power of 600 mW a trap depth of 120 µK is realized. After switching off the 689 nm MOT up to 106 atoms at 3 µK are trapped in the lattice. This corresponds to a transfer efficiency from the 461 nm MOT into the lattice of up to 3%.

f = 30 mm

λ/2plate polarizer

f = 300 mm

pump laser 10 W

Ti:Sa 1.1 W813 nm

optical fiber

mechanicalshutter

gravity

dichroicmirror

clock laserbeam (698 nm)

f = 300 mm

Fig. 1.2. 3: Setup of the 1D optical lattice at 813 nm. The one dimensional (1D) lattice is directed perpendicular to gravity and to the axis of the MOT coils.

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The loading of the optical lattice with strontium atoms from a magneto-optical trap (MOT) is an essential preparation step. The atoms have to be cold enough to be trapped in the lattice potential of 120 µK depth. The temperature also influences, together with the value of the Lamb-Dicke parameter, the excitation rate: in excited vibrational levels of the lattice potential the atoms are less confined than in the ground state because of the extended vibration amplitude. At typical temperatures of 3 µK 90% of the atoms are in the ground state of the oscillation along the lattice beams. The atom number must be high enough to ensure sufficient signal-to-noise ratio for clock operation while the loading needs to be fast to achieve high stability. For the present investigations, the time component of the optimization is of small importance, but high atom numbers are desirable to evaluate systematics at high density. The loading was optimized presently for this purpose. The timing of the experimental cycle is depicted in Fig. 1.2.2. We have observed that the atom number in the optical dipole trap can be optimized by the duration of the last cooling stage, which is the single frequency cooling on the intercombination line (Fig. 1.2.4). The red curve is a fit according to a simple model, which describes the evolution of the atom numbers Ndip and NMOT under exchange of atoms between the dipole trap and in the MOT:

)(1)()(

* tNtNRt

tNdipMOT

dip

dipd

d⋅−⋅=

τ, Eq. 1

)/exp()( 0 MOTOTM τtNtN −⋅= . Eq. 2 The loading rate R describes the transfer of atoms from the MOT into the dipole trap. The dipole trap has an effective lifetime τ*

dip which includes the losses due to collisions with the background gas and the transfer back into the MOT. It will turn out that the latter is the dominant process in our setup. The lifetime of the MOT is given by τMOT and was determined independently. The model neglects the change of atom number in the MOT NMOT due to loading into the dipole trap or due to the back transfer, which is justified for the observed transfers of about 10%. From the fit we find R = 8 s–1 and τ*

dip = 28 ms being much shorter than the dipole trap lifetime without

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

N (1

06 )

Time (ms)

Fig. 1.2.4 Atom number in a running wave dipole trap as function of the length of single frequency cooling. The loading into the dipole trap can be described by a simple model (red fit curve, see text.)

MOT

MOT

dipole trapR

τMOT

τdip*τdip

43

MOT of more than 2 s. Independently, we measured τMOT = 460 ms and the initial atom number in the MOT of N0 = 8·106 atoms. This model together with data for the interrogation process and the resolvable linewidth will allow to optimize the loading for best stability of the clock. 1.2.2 Interrogation and Detection of the Clock Transition Using the 698 nm laser system with the cavity on the vibration isolation table but without the acoustic isolation box we investigate the single photon excitation of the 1S0 – 3P0 clock transition in bosonic 88Sr. For interrogation the 1S0 – 3P0 clock transition, the light of the 698 nm slave laser is superimposed with the 1D optical lattice. The beam has a waist radius of 40 µm. To enable the 1S0 – 3P0 clock transition in bosonic 88Sr, which is forbidden for any single photon transition, we follow the proposal by Taichenachev et al. [Taichenaev2006] and apply a dc magnetic field for mixing a small and controllable fraction of the nearby 3P1 state to the 3P0 state. This method has been successfully employed by Z. W. Barber et al. with neutral 174Yb [Barber2006] and by X. Baillard et al. with 88Sr [Baillard2007]. The magnetic field is oriented parallel to the linear polarization of the interrogation laser beam. For spectroscopy of the 1S0 – 3P0 transition, the coupling magnetic field of 2.3 mT is turned on and a 200 ms long pulse of the 698 nm interrogation laser with an intensity of 3.2 W/cm2 excites a fraction of the atoms into the 3P0 state. The 461 nm MOT beams are then used to detect the remaining ground state atoms by their fluorescence.

-500 0 500 1000 1500 200050

75

100

125

150

175

num

ber o

f 1 S 0 ato

ms

(arb

. uni

ts)

Relative frequency (Hz)

165 Hz

Fig. 1.2.5: Magnetically induced 1S0 – 3P0 clock transition of 88Sr. Each data point corresponds to a single measurement cycle of 640 ms. The frequency axis is determined from the offset between the reference cavity and the interrogation laser (twice the AOM frequency). It is corrected for the cavity drift and shifted by an arbitrary frequency to obtain small numbers.

Fig. 1.2.5 shows the variation of the fluorescence signal with respect to the interrogation laser frequency. The cycling time of the frequency scan is given by the duration of the cooling stages, the probe pulse and the fluorescence detection, which sums up to 640 ms. With a Lorentzian line fit to the measured spectrum we get a FWHM linewidth of 165 Hz. The difference to the laser linewidth deduced from the virtual beat is most likely due to different environmental conditions,

44

e.g. no acoustic isolation box was used during the spectroscopy. To achieve better resolution in future measurements, it is necessary to improve the probe laser linewidth. This is achieved by phase locking the laser to the 657 nm reference laser as described in the next section. Two repumping lasers at 707 nm (3P2 - 3S1) and at 679 nm (3P0 - 3S1) have been set up that allow to repump atoms from the upper clock state 3P0 back to the ground state. This now allows also the detection of the number of excited atoms (Fig. 1.2.2). Thus we now can obtain full knowledge of the excitation process of the clock transition. For future investigations on 87Sr a 689 nm “stirring laser” [Mukaiyama2003] has been set up, that is required for efficient operation of the second MOT stage with this isotope. The laser consists of an 689 nm extended cavity diode laser that is electronically phase locked to the 689 cooling laser with a frequency offset of 1.4 GHz. Currently measurements of the trap parameters (density, temperature) and of Rabi oscillations for various trap conditions are under way, which will lead to an improved determination of systematic frequency shift in an optical lattice clock. 1.2.3 Performed Tests The tests on loading of the lattice was performed and modeled by a differential equation as explained in the sections above. Investigation of collisions as important input parameter for a lattice design for 88Sr is currently under way.

45

46

Workpackage 1.3 - Strontium pre-cooling laser (LENS) This workpackage is intended to provide the laser radiation for the cooling stage of strontium vapors and for the detection of the atoms in the electronic ground state. A scheme of the blue laser, emitting on the 1S0-1P1 strontium transition at 461 nm, is reported in Fig. 1.3.1. The source is based on frequency doubling of an high power semiconductor 922 nm laser.

Fig. 1.3.1 Experimental setup for the blue (461 nm) laser. Left: optical schematic. Right: physical size of the laser source. Bottom: picture of the pre-cooling laser source assembled at LENS. More than 300 mW at 461 nm are obtained by frequency doubling of a high power semiconductor 922 nm laser in a non-linear crystal. Improved output power stability and frequency stability make this laser source suitable for cooling and trapping Sr atoms (see text for details). ECDL extended cavity diode laser, TA Tapered amplifier, OI optical isolator, BIBO bismuth triborate nonlinear crystal, SHG second harmonic generation cavity; MOPA tapered amplifier. The 922 nm laser is based on a low power external cavity diode laser (ECDL) which is amplified to about 1.2 W on a semiconductor tapered amplifier. The ECDL, which delivers about 30 mW continuous wave, has a spectral linewidth less than 500 kHz, and the latter remains constant after the optical amplification stage [Ferrari1999]. After frequency doubling the resulting spectral

47

linewidth is less than 1 MHz and, as required in the workpackage, it is substantially smaller than the 32 MHz natural linewidth of the atomic transition addressed with this laser. In order to maximize the overall stability of the system and insure the reliability in the long term, two optical isolators are installed in the fundamental laser source. A 60 dB optical isolator between the ECDL, playing the role of the master laser, and the semiconductor tapered amplifier prevents optical feedback in the ECDL, which otherwise could result in frequency instabilities. A 35 dB optical isolator after the tapered amplifier prevents accidental back reflections into the amplifier which could lead to permanent damages. The fundamental laser head will be assembled in box 53 cm long, 15 cm wide, and about 10 cm height, and it will directly provide the radiation to the frequency doubler. The frequency doubler is based on second harmonic generation on a bismuth triborate nonlinear crystal (BiBO) through type I critical phase matching. Since the single pass conversion efficiency would not insure the blue power requested in W.P. 1.3, the nonlinear crystal is placed inside a bow-tie cavity which is kept resonant to the 922 nm laser field resulting in as much as 40 W effective field incident on the crystal. In the end this insures about 25 % optical-to-optical conversion efficiency in the frequency doubling process, and a about 300 mW of blue laser radiation. The optical setup of the frequency doubler has been tested addressing both the issues of reliability on the long term operation in a laboratory environment, and the capability to do spectroscopy and frequency stabilize the laser on the relevant atomic optical transition. The complete system shows a stability on the daily operation, and a repeatability from day to day well beyond the typical conditions required for the operation of the final optical clock. As an example we report in Fig. 1.3.2 a typical curve of the power stability of the blue laser on a 10 hours timescale. On shorter timescales the blue laser shows a 1.5% rms noise which is mainly due to the acoustic noise generated by the external and independent electronic devices operating in the room where the measurements were performed. Fig. 1.3.2 Typical power stability of the blue (461 nm) laser on the timescale of several hours. The fluctuations at the level of 1.5 % peak-to-peak are ascribed to the environmental thermal fluctuations of 2 Celsius peak-peak, which induce drifts on the fundamental laser power (922 nm) and the frequency doubler conversion efficiency. A preliminary test of the spectral properties of the blue laser was performed by addressing the atomic transition on strontium vapor, with sub-Doppler spectroscopy, and frequency stabilizing the laser to the transition of the most abundant 88Sr isotope. As reported in Fig. 1.3.3, the blue laser allows obtaining a clear signal both on the Doppler profile, where the width of about 1.5

48

GHz is set by the temperature of the atomic gas in the heat pipe (630 Kelvin), and the saturation spectroscopy signal for both the 86Sr and 88Sr isotopes can be resolved. Using saturation spectroscopy and applying frequency modulation techniques we can obtain the signal suitable to frequency stabilize the blue laser on both of the 86Sr and 88Sr isotopes. A test of frequency stability under locked condition has also been performed. The result shows that the laser can operate continuously for several hours without unlocking from the atomic signal. The final frequency doubler head is assembled in a box 39 cm long, 22 cm wide, and about 10 cm high (Fig. 1.3.1). The described laser source has been successfully used to cool Sr in a laboratory apparatus (not part of this project), in which also spectroscopy of Sr atoms in an optical lattice was achieved.

Fig. 1.3.3 Laser spectroscopy with the laser source realized in W.P. 1.3. The spectra are obtained by saturation spectroscopy on strontium vapors on the 1S0-1P1 transition at 461 nm. Centered on the 1.5 GHz broad Doppler absorption line the 88Sr sub-Doppler peak is observable. By applying frequency modulation techniques it is possible to recover the signal suitable to frequency stabilize the blue laser on both the 86Sr and 88Sr isotopes (see inset).

49

50

Workpackage 1.4 - Transportable cold Strontium source (LENS) The cold atom source represents the core of the Strontium transportable clock. Sr atoms need to be pre-cooled and trapped before the interrogation of the clock transition. With this system it will be possible to trap Sr isotopes at a final temperature of about 1mK. Furthermore, the setup will be compatible with second-stage cooling and for optical trapping of Sr isotopes. The design of the complete apparatus (WP1.3 and WP1.4) mounted on a single 120x90 cm breadboard is presented in Fig. 1.4.1. Main components of the system are: pre-cooling laser at 461 nm (see previous section WP 1.3), breadboard for production of frequencies needed for frequency stabilization of the laser source itself and for cooling beams (MOT, Zeeman slower, 2D molasses), and the vacuum apparatus. More details on each component are reported in the following sections.

Fig. 1.4.1 Artist’s view of the final transportable setup composed of the pre-cooling laser (front right, WP1.3), the vacuum setup for the magneto optical trap (back half, WP1.4) and the compact breadboard (front left, WP1.4) used to produce the optical frequencies for cooling and trapping Sr.

51

1.4.1 Compact breadboard for frequency production Starting from the master pre-cooling source several different laser frequencies are needed for cooling and trapping Sr atoms. In particular, three different laser detunings are necessary respectively for MOT beams, Zeeman slower beam and for 2D transverse cooling, and other two are used to probe the atoms in the ground state and to frequency-stabilize the laser source. All the frequencies can be produced by the use of acousto-optical modulators (AOM) that shift the frequency of the laser beam coming from the source and provide an independent control of the power of each beam. A new design of the optical system needed for cooling Sr has been done (see Fig. 1.4.2). The breadboard has been designed following the approach of compact and ultra-stable opto-mechanical mounts developed for transportable systems in FINAQS and ESA-SAI projects [Finaqs03,Sai04]. The breadboard geometry is 30 x 40 x 6 cm and it fits on a side of the Sr compact breadboard.

Fig. 1.4.2 Artist’s view of the compact breadboard for the production of frequencies for cooling and trapping strontium atoms. The breadboard is connected with optical fibers to the pre-cooling laser and to the transportable Sr vacuum system. The breadboard dimensions are 30 x 40 x 6 cm (including mounts’ height). Two independent beams coming from the pre-cooling laser, are delivered with single mode fibers to the breadboard. As discussed earlier, the five beams produced in the breadboard are respectively used to stabilize the frequency of the master source through spectroscopy on 1S0-1P1 transition, and to provide the proper optical power and frequencies for the 2D molasses, magneto-optical trap, Zeeman slower and probe beam (see Fig. 1.4.3 for a frequency chart).

52

Fig. 1.4.3: Frequencies chart for the single-stage Sr MOT. The beam coming from the master source (at -150 MHz) is shifted in frequency by the use of single-pass and double-pass acousto-optical modulators.

The five outputs of the breadboard are then coupled into single-mode fibers and delivered to the vacuum system. The first two beams are used in the first part of the vacuum setup (left side of the apparatus, Fig. 1.4.4), the oven region. Here, a resonant probe beam is sent through two CF16 optical access windows to do spectroscopy on the 1S0-1P1 transition, while the second beam is sent through the rectangular windows after a mechanical shutter for the 2D molasses. Then, the MOT beam is coupled into a fiber splitter that divides the input power into six independent beams. The fiber splitter has a second input port which can be used to couple the 689 nm light needed for the second stage cooling. The two colors are coupled together with the use of an internal dichroic plate. Polarization control and expansion of the two color beam is done with broadband optics. Finally, the Zeeman slower beam is coupled to the vacuum system though the sapphire window at the end of the beam (right side of the apparatus, Fig. 1.4.4), and aligned collinear with the atomic beam. One of the small CF16 windows will instead be used for the probe beam. 1.4.2 Vacuum apparatus In Fig. 1.4.4 is reported a picture of the vacuum apparatus for the Sr transportable clock under development at LENS. Main components of the Sr setup are the oven, the 2D molasses region, the Zeeman slower and the MOT cell.

53

Fig. 1.4.4 Schematic of the vacuum apparatus for the Sr transportable optical clock. Strontium is evaporated in the oven at the right side of the apparatus. The new oven developed at LENS is based on a commercial ‘getter’ source, filled with Strontium. The source is very compact and as reported in Fig. 1.4.5 can be easily mounted on a standard CF40 vacuum cube. Preliminary tests have shown that under normal operation the power consumption is only 4 W. The geometrical divergence of the Sr beam is of the order of 20°.

Fig. 1.4.5 New compact and low power consumption source of vapours of atomic strontium. On normal operation only 4 W are dissipated on the heating electrodes. The source under study has been mounted on a standard CF40 cube. A first collimation of the Sr atomic beam is done by a 4 mm orifice placed in the middle of the oven region. Here, a mechanical shutter placed between the oven and the orifice will be used to stop the atomic beam during the spectroscopy phase after the loading of the Sr trap. A second collimation of the beam is done in the next region of the oven. Here, the transverse velocity of the atoms is reduced by a 2D molasses placed right after the orifice. As discussed earlier, inside the oven it is possible to use additional optical access to the beam in order to

54

perform spectroscopy on the 461 nm transition. The spectroscopy signal is necessary to stabilize the frequency of the pre-cooling laser source. The atoms then travel along the Zeeman slower region where the combined action of the magnetic field produced by a 10 cm long solenoid and a counter-propagating resonant light beam reduces the longitudinal velocity of the atoms before the capture in the MOT cell. Slowed Sr atoms are then collected in the MOT cell. The MOT cell has eight CF40 windows and sixteen CF16 windows antireflection coated for visible and infrared light covering wavelength from 450 nm to 830 nm with <1% losses. The MOT beams for the first and second stage cooling are delivered with fiber coupled beam expanders that are fixed to the MOT cell. Other optical access can be used to couple infrared (813 nm) trapping light and clock light (698 nm), the probe resonant beam and repumper light (either 707 nm and 679 nm or 497 nm light). One additional CF40 access will be used to collect the fluorescence with a PMT module. A detail of the MOT cell is reported in Fig. 1.4.6. In order to reduce the power dissipated on the magnetic field MOT coils a CF200 flange with an optimized profile has been developed. A housing for the coils near to the MOT centre is extracted. With this geometry the MOT coils can provide a field gradient up to 50 gauss/cm with only 40 W of power dissipation.

Fig. 1.4.6 Detail of the MOT cell showing the modified flange (in green) that supports the MOT coils (in red) and two CF40 windows. The magnetic field of the Zeeman slower has been also optimized to match the off-axis magnetic field produced by the MOT coils. With a detuning of 325 MHz it is possible to slow atoms up to 300 m/s down to 50 m/s. The Zeeman slower coils dissipate in total only 4 W. To dissipate the heat produced by both Zeeman slower coils and MOT coils no water cooling is needed, thus reducing the setup complexity.

55

Fig. 1.4.7 Simulation of the longitudinal atomic velocity in the Zeeman slower. Atoms with longitudinal velocity of 300 m/s are slowed down to 50 m/s below the capture velocity of the MOT.

Two ion pumps are necessary to pump independently the MOT cell and oven. To improve the pumping speed and to ensure a UHV regime in the trapping region an additional Titanium sublimation pump has been installed. These two regions of the vacuum apparatus are connected by a vacuum valve. At the right end of the vacuum apparatus, a sapphire window (c-cut) will be used to couple the Zeeman slower laser beam.

56

Workpackage 1.5 - Sr clock laser (PTB) 1.5.1 Design and construction of a transportable reference resonator For a transportable cavity in addition to the general requirements of seismic insensitivity and low thermal noise also small size and low mass have to be taken into account. For a strontium lattice clock we consider a reference cavity of length L = 100 mm and diameter 60 mm. At the optical frequency of 429 THz a change of the mirror separation of 1 pm, i.e. a relative change ∆L/L = 10-

11 leads to a frequency change of 4.29 kHz. To reach the required frequency instability of 1 Hz, the design and the mounting of the cavity was optimized to make the length most insensitive to external forces acting on the spacer. In addition to this requirement, during transport accelerations above 5 g are expected. Thus a rigid mount is required that prevents the cavity from moving. On the other hand during operation a vibration-insensitive mount is required, which should avoid any additional forces that could lead to deformations and subsequent frequency changes. Two alternatives were taken into account:

1: using a proven vibration insensitive mount that is not transportable and add an additional lock mechanism to fix the cavity during transportation.

2: designing a vibration-insensitive mount that is sturdy enough to withstand also big accelerations during transportation.

From various aspects that are discussed in detail in the corresponding technical note, we have decided to follow the 2nd approach, designing a mount that holds the cavity in a reliable, well defined way, but also minimizing its susceptibility to seismic noise. Various designs with horizontal and vertical orientation of the optical axis have been compared and finally the most promising design was chosen for the prototype. A prototype cavity of 100 mm length made from ultra low expansion (ULE) glass was built. The optical axis of the cavity is oriented horizontally. A cavity finesse of 330 000 has been measured, corresponding to a linewidth of 4.5 kHz. To minimize the sensitivity against vertical vibrations, the cavity is supported at four points near to its horizontal symmetry plane [Nazarova2007]. The positions were optimized by finite element calculations. To ease the construction, we have glued four 10 mm x 10 mm invar plates on the spacer surface. A 4 mm hole was drilled into each plate and a Viton cylinder extend into this hole to support the cavity (see Fig. 1.5.1).

Fig. 1.5.1: Cavity design with mounting plates attached and detail of the mount (right)

Once the cavity was placed inside its vacuum enclosure, the sensitivity to vibrations was measured by manually shaking the setup. The corresponding frequency fluctuations and the

57

acceleration were measured simultaneously (Fig. 1.5.2). From the ratio of the two measurements a sensitivity of about 140 kHz/ms-2 to vertical vibrations was measured, which is far bigger than calculated from a finite element analysis. A difference of 1 mm from the optimal support point positions would result in a residual sensitivity of less than 8 kHz/ms-2. Thus the observed sensitivity cannot be explained by tolerances of the support point positions. We therefore attribute the discrepancy to the spacer touching the surrounding heat shield. This will be corrected in the near future.

2 4 6 8 10-10

-5

0

5

10

acce

lera

tion

[mm

/s2 ]

time [s]2 4 6 8 10

6

8

10

12

14

16

18

20

frequ

ency

[kH

z]time [s]

Fig. 1.5.2: Acceleration (left) and corresponding frequency changes of the 698 nm laser (right) for axial accelerations of the reference cavity.

The cavity is mounted in a vacuum chamber made from a CF100 tube, which is held at a residual pressure of 10-7 mbar by a 2 l/s ion getter pump. The vacuum chamber is put in a temperature-stabilized aluminium tube that is heated by resistive heaters to 25°C. Temperature fluctuations of the cavity are further reduced by a gold plated copper tube placed around the cavity inside the vacuum chamber that acts as thermal shield. The measured thermal expansion zero-crossing temperature of the ULE spacer material is at 10°C. Therefore temperature fluctuations still change the optical frequency with rates of up to 1 Hz/s. To operate the cavity at its zero-crossing temperature and to perform measurements of its thermal expansion properties, a second vacuum chamber with thermoelectric coolers was used. The Peltier elements are put between the walls of the vacuum camber and the internal heat shield. With moderate electric power of 3.5 W the inside could be cooled to 10°C. With low sensitivity to seismic noise, the frequency stability for averaging times between 1 s to 100 s is now mostly limited by thermal noise of the mirror separation due to Brownian motion of the spacer, the mirror substrate and the mirror coating [Numata2004]. Here materials with higher mechanical quality factor Q are advantageous. Especially, using mirror substrates made from fused silica it is expected to reduce the thermal noise floor from σy = 7.2·10-16 to σy = 3.3·10-16. The drawback is the large thermal expansion coefficient of these mirrors that can deform the cavity. From finite element simulations we calculate, that this temperature dependent deformation will shift down the zero crossing temperature by 20 K. This increased thermal expansion sensitivity was confirmed by measurements using the Peltier chamber, as shown in section 1.5.4. 1.5.2 Setup of the transportable clock laser

For probing the 1S0 – 3P0 strontium clock transition we have set up a 698 nm cavity stabilized master-slave diode laser system as shown in Fig. 1.5.3 and Fig. 1.5.4. The cavity and laser setup

58

follows the design of our 657 nm laser [Stoehr2006]. For reducing seismic noise the cavity is placed on a vibration isolation platform inside an acoustic isolation box. Because of limited space and to avoid disturbing the isolation system both lasers are placed on a separate 60 cm × 90 cm breadboard. A short polarization maintaining single mode optical fiber of 1.5 m length links the master laser with the cavity setup. As was shown in the similar setup of the 657 nm laser the vibrational and thermal fiber noise is not limiting the master laser stability at the level of 1 Hz linewidth.

faraday-isolator

reference cavity PDH-detector

polarization maintainingsinglemode optical fiber

vibration isolation platform

AOMl /4

master

laser-diode

PBS

grating1200/mm

piezo-mirror

local oscillator14.3 MHz~

faraday-isolator

vacuum chamberphase

modulator

slavefaraday-isolator to strontium atoms and

femtosecond fiber comb

laser-diode

servo electronics

Fig. 1.5.3: Setup of the master-slave diode laser system for probing the strontium clock transition.

The master laser is an extended cavity diode laser (ECDL) in Littman configuration operated at a diode temperature of 44 °C with an output power of 4 mW. Its output frequency is locked to a high finesse optical cavity by the Pound-Drever-Hall (PDH) [Drever1983] stabilization technique. An acousto-optic modulator (AOM) introduces a frequency offset for tuning the laser.

The injection-locked slave laser delivers an output power of 23 mW. The laser remains injection-locked over several days without manual resetting and adjustment. Its light is sent to the strontium atoms and to the femtosecond fiber-laser comb by two optical fibers with provisions to cancel noise acting on the fiber length [Ma1994].

59

Fig. 1.5.4: Clock laser setup.

1.5.3 Measurements of frequency stability A commercial femtosecond fiber-laser comb was used to characterize the laser system in comparison to a well characterized 1 Hz linewidth laser at 657 nm. We used the femtosecond laser as transfer oscillator [Telle2002, Grosche2008] as shown in Fig.1.5.5 to compare the optical frequencies νCa and νSr of the 657 nm Ca laser and the 698 nm Sr laser.

νSr m1 frep-

m1m2

( )νCa m2frep-

virtual beatDDS

:2

∆Ca= ( )νCa m2frepνCEO +- 2

∆Sr= ( )νSr m1 frepνCEO+- 2

21

21

νCaνSr - m1m2

( )21

( )

:2

νCEO

Fig. 1.5.5: Schematic of the rf electronics for generating a virtual beat signal between the strontium and the calcium laser. The fs-comb acts as a transfer oscillator. Thus the virtual beat is independent of fluctuations of the repetition rate frep and the carrier envelope offset frequency νCEO of the femtosecond fiber comb.

For each laser the beat signal ∆Ca and ∆Sr with the neighboring comb line is detected. These beats are generated with the frequency-doubled output of the comb. Thus, the frequencies of the comb lines are given by the product of the integer mode number m and the repetition rate frep plus twice the carrier envelope offset frequency 2νCEO, which is measured with a f – 2f interferometer using the original fs-laser output. Each beat signal is pre-processed by a tracking oscillator and digitally divided by two. Then νCEO is removed from both signals by multiplying them with νCEO in a mixer and selecting the sum frequency. The signal frequency in the calcium branch is multiplied

60

by m1/m2 using a direct digital synthesizer (DDS). After subtracting the frequencies, one obtains a signal that corresponds to a virtual beat of the two optical frequencies νSr/2 and νCa·m1/2m2. This signal follows the frequency fluctuations of both lasers with a bandwidth of several tens of kilohertz, limited by the bandwidth of various phase-locked loops used to track the intermediate frequencies. This virtual beat has a frequency of around 26 MHz. Since it is independent of frep and νCEO it is not degraded by fluctuations of these two quantities within the tracking bandwidth.

-2000 -1000 0 1000 2000-70

-60

-50

-40

-30

-20

-10

0

10

f0 = 26 MHz

30 Hz

S

pect

ral p

ower

(dB

m)

f - f0 (Hz)

no isolation vibration and acoustic isolation

270 Hz

RBW = 30 Hz

Fig. 1.5.6: Frequency spectrum of the virtual beat between the 698 nm Sr laser and the Ca reference laser. The spectrum obtained without any isolation (270 Hz linewidth) was averaged over 10 sweeps of 0.135 s. The spectrum measured with a passive vibration isolation table and acoustic isolation (30 Hz linewidth) was averaged over 100 sweeps.

The resulting beat at νSr/2 is shown in Fig. 1.5.6. The resulting linewidth at νSr is between 2 and 4 times as large, depending on the spectrum of the frequency noise [Elliot1982]. As the linewidth of more than 60 Hz is too large to for the measurements of WP 1.2, and opening the vacuum chamber would interrupt the whole experiment, we decided to reduce the linewidth of the 698 nm laser by locking its frequency to the ultrastable 657 nm laser. To perform this phase lock of the 698 nm diode laser system to the 657 nm reference laser, the virtual beat signal between both lasers is compared with the output of an rf-synthesizer by a phase and frequency comparator (Φ, Fig. 1.5.7). The rf-synthesizer is referenced to a 100 MHz signal derived from a H-Maser. The comparator output drives a high quality surface-acoustic wave (SAW) 400 MHz voltage controlled oscillator (VCO). A DDS is used to transform this signal to the frequency of 266 MHz driving the double-pass AOM between the Sr master laser and the reference cavity. The rf-frequency at the AOM controls the Sr laser frequency and therefore the virtual beat frequency, thus closing the phase-locked loop.

61

:4

:4

Φ VCO

DDS

Ca laser

fs-comb

Sr laser

12 ( )νCaνSr-

m1m2

rf-synthesizer

AOMreference

cavity

Fig. 1.5.7: Schematic of the phase-lock of the 698 nm Sr laser to the 657 nm Ca laser serving as a reference.

Fig. 1.5.8 shows the spectrum of the virtual beat at 26 MHz with the PLL of the 698 nm Sr laser open and closed, respectively. Without the PLL the laser showed a linewidth of a few hundred Hertz caused by seismic and acoustic vibrations of the reference cavity; with open PLL we observe frequency noise of the free-running VCO. When the phase-locked loop is closed, the virtual beat signal narrows down to a δ-function. The measured linewidth of the virtual beat of 1 Hz is then limited by the resolution bandwidth of the spectrum analyzer. This indicates that the stability and linewidth of the 1-Hz linewidth 657 nm laser has been transferred to the strontium clock laser.

-40 -30 -20 -10 0 10 20 30 40-60

-50

-40

-30

-20

-10

PLL on

Spe

ctra

l pow

er (d

Bm

)

f - f0 (kHz)

RBW = 100 Hzf0 = 26 MHz

PLL off

Fig. 1.5.8: Virtual beat between Sr and Ca laser with the phase-locked loop (PLL) open and closed. With the PLL open the noise of the free running VCO is dominating. Both spectra are averaged over 10 sweeps with a sweep time of 80 ms.

62

1.5.4 Performed tests Tests of cavity designs are ongoing, results are shown in the above section. The thermal sensitivity was measured, especially when the mirrors are replaced by fused-silica mirrors that provide less thermal noise. The results of Fig. 1.5.9 show that by replacing only one ULE mirrors by a fused silica mirror, the zero-crossing temperature of the total cavity thermal expansion is shifted from 21°C to 11°C. Thus replacing both mirrors would shift the zero crossing temperature by 20 K to lower temperatures.

5 10 15 20 25 30 35 40 45-100

0

100

200

300

400

500

600

α(T) = a*(T-T0)+b*(T-T0)2

∆L/L=L0+a/2*(x-T0)^2+b/3*(x-T0)^3+d*(t-t0);

Data: extract_EModel: CTE_T0_drift_Weighting: y No weighting Chi^2/DoF = 0.03556R^2 = 0.99999 L0 -25.09919 ±0.04285T0 21.30511 ±0.00248a 2.53711 ±0.00161b -0.01421 ±0.00013d 0.03982 ±0.00089t0 54259 ±0

∆L/

L (p

pb)

T (°C)

L=103 mmMay 2007

lin driftresiduals * 2

8 10 12 14 16 18 20 22 24 26 28 30 32 34-200

-100

0

100

200

300

400

500

Daten: extract_EModell: cteGewicht:y Keine Gewichtung. Chi^2/DoF = 0.83203R^2 = 0.99997 L0 -112.74343 ±0.46874T0 11.15914 ±0.06577a 2.69199 ±0.04398b -0.01481 ±0.00228d -0.0181±0.01292t0 54548.86221 ±--

α(T) = a*(T-T0)+b*(T-T0)2

∆L/L=L0+a/2*(x-T0)^2+b/3*(x-T0)^3+d*(t-t0);

∆L/

L (p

pb)

T (°C)

with FS mirrorL=103 mmApril 2008

Fig. 1.5.6: Thermal expansion of spacer with two ULE mirrors (left) and with one mirror replaced by a fused-silica mirror.

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Long term tests and temperature sensitivity of the complete laser setup is planned for the future – especially when the laser is transported to perform measurements outside PTB.

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Workpackage 1.6 - Sr clock characterization (SYRTE) 1.6.1 Short-term stability assessment by comparison with second optical lattice clock As stated above, the main contribution to the clock instability is the frequency noise of the clock laser probing the clock transition. Assessing the short term stability of a Sr lattice therefore implies the development of a very stable clock laser, by pre-stabilisation to a high finesse cavity.

Fig. 1.6.1: Cut-view of the new ultra-stable cavity design (see text for explanation). In the classic approach, the laser is stabilized to a cylindrical optical cavity supported by V-shaped blocks. In this configuration the frequency stability can be limited by the level of vibration which induces length fluctuations. The vibration level can be minimized using a vibration isolation system. However the residual vibration noise of commercial systems is still insufficient to reach Sub-Hz level laser linewidth. Several groups have proposed and successfully realized low-g sensitive cavity [Rosenband2004,Nazarova2006,Ludlow2007,Webster2008]. Following the mainstream of those results, we developed two different designs of cylindrical cavities. The intensive use of Finite Elements software (FEM) and multiprocessor computational power allow an extensive and refined study of the vibration response of these two designs: a vertical and a horizontal geometry.

The first one is a 100 mm long vertically mounted cylindrical cavity. The contact plane is obtained machining a shoulder in the spacer. The vibration sensitivity depends on the ratio diameter/length, the position of contact plane and the geometry of the shoulder.

The second one is a 100 mm long cavity held horizontally. This configuration allows a fine adjustment of the positions of the four supporting points in order to experimentally minimize the vibration sensitivity. Beyond the necessary evaluation of the vertical axis vibration sensitivity, a considerable part of the work has been devoted to horizontal sensitivities because the residual horizontal vibration level can be the dominant source of noise in commercial anti-vibration tables. The spacers of the two cavity configurations are machined from Ultra Low Expansion glass rods (ULE). The cavities show finesses of about 700 000 and a fringe contrast better than 50%. The substrates of the mirrors are made from fused silica in order to reduce the

Thermal shields

Inner vaccum chamber

Outer vacuum chamber

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contribution of thermodynamic noise limit [Numata2004]. This fundamental limit is a fractional root Alland variance ~ 4x10-16

for a 100 mm long cavity with fused silica mirrors compared to ~1x10-15

for an ULE substrate. However fused silica exhibits a much larger temperature coefficient than ULE. The overall temperature coefficient of the optical cavity is much larger than that of an all-ULE cavity and the temperature of zero thermal expansion coefficient is shifted well below 0°C. This increased temperature sensitivity requires a more sophisticated design of the cavity environment. A high thermal shielding factor coupled with a tight temperature control is necessary to minimize the impact of temperature fluctuations on cavities. The thermo-mechanical setup of the vacuum cavity enclosure for the horizontal cavity is shown in Fig. 1.6.1. It includes four gold coated aluminium thermal shields and a double-shell vacuum chamber to avoid water condensation on windows at low temperature. Two laser beams were stabilized to two independent cavities using the Pound-Drever-Hall technique. The beat-note signal between the two stable lasers is demodulated by a frequency-to-voltage converter and analysed with a Fast Fourier Transform analyser. For each cavity we measured the three vibration sensitivity coefficients by shaking the cavity set-up with sinusoidal signals in the frequency range 1-10 Hz. A low-noise seismometer placed on the top of the vacuum chamber measured the accelerations on the tree spatial directions. We excited sequentially the two horizontal and the vertical directions and measured the amplitude of the induced frequency tone and the strength of the acceleration. Both cavity geometries have vibration sensitivity coefficients lower than 1x10-11/(m.s-2) (Fig. 1.6.2). These results are better than the previous published results, moreover in the case of the horizontal geometry, the design shows a very low dependence on the supporting point position (1.6x10-12/(m.s-2) per mm). A preliminary comparison between vertical and horizontal cavity already shows a frequency instability lower than 2x10-15 for a one second averaging time (Fig. 1.6.3). The ultimate frequency stability of our system is expected to be in the mid - 10-16 , limited by the thermal noise.

Fig 1.6.2: Measured (green circles) and calculated (blue triangle, black stars, red squares) acceleration sensitivity along the vertical axis as a function of the distance between the support point of the cavity and the end mirror, for the horizontally mounted cavity. The calculation was performed for three different effective sizes of the support points: 4 mm2 (blue triangles), 1 mm2 (red squares) and 0.2 mm2 (black stars).

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Fig. 1.6.3: Frequency stability of the beat note between two independently stabilized Strontium clock lasers. The fractional root Allan variance is less than 1.5 x 10-15 for the integration times 1-10 s relevant for the operation of the optical clock. 1.6.2 Longer-term evaluation/comparison with microwave fountains Preliminary experiments have been performed to assess the long-term frequency stability and to evaluate the accuracy of the Sr clock. The present frequency stability of the clock is determined by the stability of the clock laser. Fig. 1.6.4 shows the Allan deviation of the comparison between the Sr optical lattice clock and an microwave cold atom fountain clock. This gives σy(τ)=6 x 10-

14τ-1/2, with roughly equal contributions from the Sr clock and from the fountain. After 1 h of averaging time, the frequency noise of the measurements averages down to 10-15, which corresponds to a frequency resolution of 0.5 Hz for the optical clock. This measurement was performed prior to the new cavity realization described in Section 1.6.1 and we expect a very significant improvement when this laser can be used. The main limitation should then be due to the atomic fountain frequency noise, at a level of 3 to 4 x 10-14τ-1/2.

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Fig 1.6.4: Frequency instability of the Sr optical clock- Cs microwave fountain comparison.

1.6.3 Measurement of systematic effects < 10-16 Systematic effects have been evaluated with a frequency resolution of about 10-15, achievable as described above. The main studied effects are the residual light shift due to the confining optical lattice and the Zeeman effect. The light shift is inherent to the operation of this new type of clock and therefore requires specific study. The Zeeman effect is also of relevance due to the linear dependence of all the atomic transitions frequencies in the fermionic isotope used here on the magnetic field, as opposed to the quadratic dependence in more traditional microwave clocks. The overall uncertainty budget is reported in Table 1.6.1 [Baillard2008].

Table 1.6.1: Status of the Sr clock accuracy budget Interrogating alternately symmetrical Zeeman components in principle cancels the first order Zeeman effect on the average clock frequency. One then expects the clock frequency to only depend on the quadratic Zeeman effect. However, the required level of cancellation of the linear term is relatively high. In normal operating conditions (B ~ 90 µT) the linear Zeeman shift of the two symmetrical clock transitions is about 500 Hz each. For an evaluation at the Hz level (2 x 10-

15), the level of cancellation should be of the order of 10-3. We measured the clock frequency (with the cancellation technique applied) as a function of the bias field and observed no residual first-order dependence to within our measurement uncertainty. Up to a field of ~10 G, the clock

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frequency exactly follows the expected quadratic dependence. Under normal operating conditions, this second order Zeeman frequency shift is ∆Z= -0,15 Hz, corresponding to a correction of +0.15 Hz of the clock frequency. The frequency shift due to the lattice has been extensively studied. A measurement campaign has been specifically dedicated to the measurement of the magic wavelength which is presently known with an accuracy of 10-3 nm: λm=813.428(1) nm [Brusch2006]. This experimental determination was performed by measuring the clock transition light shift as a function of the lattice wavelength. The frequency shift due to the atomic hyperpolarizability with its quadratic dependence on the lattice depth was also measured. It turns out that scaled down to a lattice depth of 10 Er, this frequency shift is -1(1)x10-18, which ensures the feasibility of high accuracy clocks based on lattice confinement. The present level of control of the lattice-induced shift is such that no change in the atomic frequency is observed, for depths ranging from 50 Er to 500 Er. The light shift of individual clock states ranges up to 1.8 MHz. If one scales the effect linearly down to 10 Er, the frequency shift reduces to 2(2) x 10-17, already very close to the ultimate expected accuracy for the Sr lattice clock. Finally, we have measured the frequency of the Sr clock transition to be:

ν(87Sr)=429 228 004 229 873.6(1.1) Hz,

with a fractional inaccuracy of 2.6 x 10-15. 1.6.4 Study of a dedicated link for comparison with PTB We have demonstrated the first ingredients towards the long distance (Distance SYRTE-Paris-PTB-Braunschweig of the order 1000 km depending on actual path followed by the fiber) comparison of optical clocks with no degradation of the clock performance. In this preliminary experiment we demonstrate the transfer of an optical frequency over a dedicated telecom optical fiber over a distance up to 172 km.

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CavityStabilized

Fiber Laser1542 nm

AccumulatedPhase noise

φc

Remote EndLink stabilityMeasurement AOM 2

AOM 1

PD 2

PLL

PD 1

PC

OC

φp

Compensation system

Local End

RF synth.

Fig. 1.6.5: Scheme of the long-distance fiber noise cancellation test system. Blue-grey boxes are fiber couplers; PD: photodiode; OC: optical circulator; PC: polarization controller. The scheme of the link test setup is shown in Fig. 1.6.5. It is based on the principle first described in [Ma1994]. The laser light to be transmitted is divided into two parts using a fiber coupler. One arm provides, after another division, the reference signal for stability measurement (leftmost vertical red line) and fiber-induced phase noise compensation, while the other arm is connected to the link through an optical circulator (OC) followed by acousto-optic modulator AOM1 (with frequency f1 ≈ 40 MHz). To compensate for the phase noise φp accumulated along the fiber, part of the signal at the remote end is reflected back to the link through an optical circulator, after frequency shifting by acousto-optic modulator AOM2 (with frequency f2=70MHz). This function is performed by the black dashed box in Fig. 1.6.5. This return signal, which passes twice through the link and experiences a phase noise 2φp, is mixed at the local end with the reference signal on photodiode PD1. The beat note at frequency 2f1+f2 is phase locked to a stable RF synthesizer using AOM1 driven by a voltage controlled oscillator. The phase-lock loop applies the correction φc=-φp to the AOM1 frequency f1, thus to the optical signal phase and consequently actively cancels the fiber-induced phase noise at the remote end of the fiber link. To magnify the dynamic range of the servo loop and hence improve its robustness, a digital frequency divider by 40 has been used just ahead of the phase detector.

The optical frequency (or phase) instability of the link is defined as the difference between the local and remote end optical frequencies (phases). It is measured on the beat-note at frequency f1+f2 provided by mixing the single-trip and the reference optical signals on photodiode PD2. Two polarization controllers (PC) are employed for optimizing the beat-note signal amplitudes. The compensation system is entirely fibered and uses only commercial off-the-shelf pigtailed telecommunications components.

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100 101 102 103 10410-19

10-18

10-17

10-16

10-15

10-14

A

llan

Dev

iatio

n

Averaging time [s]

Fig. 1.6.6: Performance of the link over a distance of 172 km. Blue triangles: Allan deviation without any compensation. Black squares, Allan deviation with the compensation active. Open triangles: system noise floor. Stars: modified Allan deviation with the compensation active when a Λ-Type counter is used for the measurement. Fig. 1.6.6 shows the fractional frequency instability of the 172-km link. The Allan deviation is about 4×10-16 at 1 second and in the range of 10-19 at 1 hour with a 10-Hz measurement bandwidth. The system floor is measured by replacing the urban fiber with an optical attenuator having the equivalent attenuation. 1.6.3 Performed tests - Test of short-term stability of both Sr clocks: not started yet. - Test of long-term stability by comparison with microwave clocks: see Sec. 1.6.2. - Reduction of (some) systematic shifts at a level < 10-16: the present status of the clock accuracy is described in Sec. 1.6.3.

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Workpackage 2.1 - Cold Ytterbium Source (HHUD-II) This workpackage is concerned with the preparation and characterization of an ultracold ensemble of Yb atoms (bosonic as well as fermionic isotopes) with a temperature in the range of some 10 µK that can be loaded into an optical lattice at the magic wavelength (760 nm) (WP 2.2.). The basic operating principle of the cold Ytterbium source is as follows.

1. A hot beam of atoms is produced in an Yb oven, 2. the atomic beam is slowed in a so-called Zeeman slower, which uses magnetic and optical

fields to slow the atoms down to velocities of several 10 m/s, 3. the slowed atoms are collected in a precooling magneto-optical trap (MOT) at 399 nm

(operating on the 1S0 → 1P1 transition) and cooled to a temperature of several 10 mK. 4. the temperature of the atomic ensemble is further decreased (to several 10 µK) and the

density increased (to 1011 atoms/cm3) in a postcooling MOT at 556 nm (operating on the 1S0 → 3P1 transition).

Since the writing of the proposal for SOC substantial changes and improvements have been made to the detailed content of this workpackage in order to optimize the outcome of the SOC project and to take into account the most recent scientific and technological developments. Most notably we have developed and set up a dedicated compact new clock apparatus which is completely independent of other experimental studies [Tassy2007, Nemitz2008] in our laboratories and has the potential for transportability. The work in this workpackage can be divided into two areas. One is development and improvement of methods in the already existing optical clock apparatus; the other is setting up and preliminary characterization of the independent, compact Yb clock apparatus. 2.1.1 Development of methods 2.1.1.1 Direct loading a postcooling MOT at 556 nm The postcooling transition 1S0 → 3P1 in ytterbium at 556 nm has a significantly broader linewidth of Γ = 180 kHz than the corresponding transition in the other optical clock candidates such as strontium, calcium or magnesium. This reduces the requirements on the laser system but also leads to a higher Doppler limit of 4 µK. Typically, the postcooling MOT is loaded from a precooling MOT. We are now routinely able to load more than 107 atoms into the postcooling MOT and achieve temperatures in the 50 µK range using this standard procedure. While generally alkaline earth atoms and similar species require three cooling stages (Zeeman slower, precooling MOT, postcooling MOT) in order to reach the temperatures and densities which are required for loading of an optical trap, it has been shown that ytterbium can be collected directly in a postcooling MOT if enough laser power (typically at least 100 mW) is available [Kuwamoto1999]. We have experimentally investigated the feasibility of this alternative method in our system using only around 10 mW at 556 nm [Nemitz2008]. Fig. 2.1. shows the loading behaviour of a directly loaded postcooling MOT with 171Yb where more than 107 atoms could be trapped after 10 s of loading. With this method the complexity of the preparation procedure may be significantly reduced, implying the possibility to build a more reliable optical clock. However, if a large repetition rate is required, as may be the case to reach the highest accuracies, it will still be necessary to use the standard cooling scheme involving a precooling MOT. The reason is that in a directly loaded postcooling MOT the loading rate is reduced by a factor of up to 100 as compared to a precooling MOT. Therefore, we regard the

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direct loading of the postcooling MOT as a valuable tool for initial characterizations but for the final layout of the optical lattice clock we will use the established three-stage cooling scheme.

Fig. 2.1.1: Postcooling Yb MOT directly loaded from a Zeeman slower. The graph shows the fluorescence at 556 nm of the trapped 171Yb during loading of the MOT. 2.1.1.2 Optical trapping of Yb As described in Sec. 2.4 , initial studies of the clock transition can be done in a postcooling MOT. However, trapping in a conservative optical trap (optical dipole trap, ODT) is required to realize an ultrahigh precision optical clock with a stability and accuracy that should ultimately reach the 10-18 level. Ultimate performance requires the storage of the atoms in an optical lattice at the magic wavelength, 759 nm in the case of Yb [Barber2006], in order to minimize the influence of the light field on the clock transition. While the setup of such an optical lattice at the magic wavelength for Yb is under way in our group (see Sec. 2.2.), we have performed precursor studies with an optical trap at 532 nm, allowing studying the general properties of the loading process and storage of an optical trap for Yb.

Fig. 2.1.2: Absorption image of 174Yb atoms trapped in an optical dipole trap at 532 nm. The image covers an area of 2.5 mm x 2.5 mm. In a typical loading sequence, a precooling MOT is loaded for 1 s before the atoms are transferred into the postcooling MOT, where they are cooled to a temperature of around 50 µK. The optical trap laser is already turned on and overlapped with the atomic cloud during this stage without any adverse effect on the MOTs. Transfer into the optical trap is realized by simply turning off the trapping light of the postcooling MOT. In the case of 174Yb, more than 2 x 105

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atoms can be transferred into an optical trap. The latter is created by focussing a 3W laser beam at 532 nm down to a waist size of 15 µm. The overall efficiency of the transfer from the precooling MOT to the optical trap is typically around 1 - 2%. A typical absorption image of an optically trapped cloud of Yb atoms is shown in Fig. 2.1.2. The elongated shape of the trapped atom cloud reflects the fact that in a single optical trap the radial confinement is typically more than 2 orders of magnitude stronger than the confinement along the axis of the laser beam. An indicator for the stability of the optical trap is the lifetime of the trap, which is determined by measuring the number of trapped atoms as a function of the holding time. This has been measured to be more than 100 s. This lifetime is consistent with a trap loss rate due to collisions with the remaining hot background gas atoms at the pressure of a few 10-11 mbar in our UHV vacuum chamber. Thus, we have no indication that any loss of atoms is induced by the trap itself, which would occur for example if excessive vibrations in the optical setup were present. 2.1.2 Set-up and characterization of a compact optical clock apparatus After completion, the compact optical clock apparatus will contain a complete vacuum system (p < 10-9 mbar), including a section for spectroscopic laser stabilization, laser systems for the Zeeman slower, the pre-cooling MOT, the post-cooling MOT, the optical lattice (WP 2.2.) and all optical components required for the operation of the MOTs and the magic wavelength optical lattice. The system will be contained on a 2 x 1 m transportable optical table and in two additional racks for electronics. In this new apparatus we have already realized a precooling MOT. For the operation of the Yb optical clock (WP 2.4.) the connection to the clock-laser section will be made via an optical fiber link and electrical cables for communication.

Fig. 2.1.3.: Optical table for the compact Yb optical clock. The table already hosts the vacuum system, the laser system for the precooling MOT, the laser system for the optical lattice and all the optics required for operation of the MOT. The empty space is reserved for the postcooling laser system and the optics that is required to shape the light fields for the optical lattice.

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2.1.2.1 Vacuum apparatus The vacuum apparatus that we have set up (Fig 2.1.4) includes four main sections:

1. A spectroscopy cell where the laser for Zeeman slower, precooling and postcooling MOT are stabilized using Doppler-reduced spectroscopy on an Yb atomic beam,

2. An Yb oven (heated to 450 °C) as a source for the atomic beam which feeds the Zeeman slower and eventually the MOTs.

3. The Zeeman slower tube in which the velocity of the Yb atoms is reduced to approx. 20 m/s in order to be able to trap them in a MOT. The Zeeman slower tube is surrounded by a tapered solenoid which creates the required position-dependent magnetic field for slowing of the atoms. For operation of the slower a laser beam which is counterpropagating with the atoms is sent into the system.

4. The main chamber in which the atoms are trapped in MOTs and then loaded into the magic wavelength optical lattice. Several solenoids are attached to the outside of the main chamber (not shown in the image) in order to create the required magnetic fields for the MOT.

Fig. 2.1.4.: Vacuum system of the transportable Yb clock apparatus. Shown is the complete system including Yb oven, spectroscopy cell for laser stabilization, Zeeman slower and the main chamber, where the Yb MOT and the optical lattice will be located. The total length of the vacuum system is approximately 1 m. The vacuum in the system with a pressure below 10-9 is maintained by two ion pumps (not shown in the image). 2.1.2.2 Diode-laser system at 399 nm The laser system for the blue MOT at 399 nm is based on recently developed laser diodes which are used in state-of-the-art data storage technology. Hereby, we rely on the availability of laser diodes with a wavelength at the edge of the production process, since the design wavelength of the laser diodes is 405 nm. Typically these laser diodes are spectrally broad (more than 10 MHz in a grating-stabilized configuration) but due to the broad Yb resonance with a linewidth of 28 MHz they can still be used for efficient laser cooling and slowing.

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The laser system that has been set up for the compact optical clock apparatus is essentially a copy of the laser system that has been successfully implemented in our stationary apparatus with the improvement that we have compactified the setup. We use one grating-stabilized laser diode which generates approx. 15 mW of output power as a master laser. The output of the master laser is split into three parts, which (after appropriate frequency shifting using AOMs) are used for frequency stabilization of the laser to a spectroscopy on an Yb atomic beam, for the Zeeman slower and as a seed for a slave laser The slave laser provides up to 30 mW of output which are used for the precooling MOT. Due to the bad transverse mode structure of the laser diodes not all of the light can actually be used for atom slowing or cooling, so that the usable power in the experiment is about 4 mW for the slower and 10 mW for the MOT.

Fig. 2.1.5.: Schematic of the diode laser based setup for the generation of the 399 nm radiation for the Zeeman slower and the precooling MOT for Yb. 2.1.2.3 Diode-laser based system at 556 nm In all experimental investigations performed so far, we have used a dye laser to generate the radiation at 556 nm for the postcooling MOT. Due to the incompatibility of a dye laser with the requirement of compactness and transportability, we have investigated alternative approaches to generate the required 10 mW at 556 nm. Since “green” laser diodes with the appropriate wavelength do not exist, the only possibility is to frequency double an infrared laser source (either a diode laser or a fiber laser) with a wavelength of 1112 nm. Since the frequency doubling efficiency scales as the square of the intensity in the fundamental, the approach for frequency doubling naturally depends on the available power in the fundamental. So far, we have investigated the following approaches:

- Single-pass doubling of a 1W fiber laser in a periodically-poled lithium-niobate crystal (PPLN). The high power available from a single-mode fiber laser together with the high conversion efficiency of PPLN allows for efficient frequency doubling in a single pass

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through the doubling crystal. In our investigations, this approach resulted in approximately 15 mW of light at 556 nm which was sufficient to operate a directly loaded postcooling MOT (see previous section). Though this approach is technically simple and fiber lasers generally have excellent spectral properties, we have discarded it due to the low reliability of the available fiber lasers at 1112 nm, which has been experienced by many research groups worldwide (According to recent news we have from industrial companies, some of the technological problems related to fiber lasers have been solved and reliable sources might be available soon).

- Resonant frequency doubling of a 100 mW grating-stabilized diode laser. Due to the lower available power, frequency doubling of diode lasers generally requires power enhancement which is obtained if the doubling process takes place in an enhancement cavity. In our first investigations we have used LBO as a doubling crystal and obtained up to several 100 µW. By optimizing and/or replacing the LBO crystal with a more efficient PPLN, it should be possible to reach the required power level. Since the laser diodes are generally more reliable than fiber lasers and resonant frequency doubling is a well controlled technique, this approach would generally meet the requirements of an optical lattice clock. Nevertheless, resonant frequency doubling adds significant complexity to the system as compared to single-pass doubling.

Since both approaches described have significant drawbacks we are currently setting up a system which is essentially a synthesis of the two:

- Single-pass frequency doubling of a 100 mW grating-stabilized diode laser in a PPLN-waveguide. This approach became possible due to the recent development of waveguide structures using PPLN. In these waveguides (6 µm x 3 µm) the light of the fundamental is guided like in a fiber and thus the intensity and the resulting frequency doubling efficiency is significantly enhanced as compared to frequency-doubling in a standard crystal. Since one test diode laser is already available and the PPLN waveguide structure is due to be delivered in the beginning of October we are planning to use this system for the realization of the postcooling MOT in the near future. We plan to later add an optically injected (slave) diode laser to the system in order to increase the available laser power in the fundamental and therefore also in the harmonic wave at 556 nm.

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2.1.2.4 Operation of a pre-cooling MOT

Fig. 2.1.6.: Fluorescing Yb atoms in a precooling MOT operating at 399 nm in the new compact optical clock apparatus. We have already succeeded in realizing a precooling MOT in the new compact clock apparatus (see Fig. 2.1.4.) using the diode laser system at 399 nm which is described above. The total laser power used for the precooling MOT is 10 mW while 4 mW are available for the Zeeman slower. The maximum numbers of captured atoms are 3 x 107 in the case of 174Yb and 1.5 x 107 in the case of 171Yb and are thus comparable to the values that have been achieved in the stationary apparatus. The relative atom numbers for the two isotopes correspond roughly to the relative natural abundances. A typical loading curve is shown in Fig. 2.1.7. The number of atoms in the precooling MOT typically saturates after several 100 ms of loading due to loss processes in the MOT because of light-assisted collisions and due to the radiative decay of the excited state into metastable states. If required, larger atom numbers and/or faster loading could be achieved by increasing the temperature of the oven which generates the atomic beam for the Zeeman slower.

Fig 2.1.7.: Loading and decay curve of the precooling MOT. The first tests on the precooling MOT in the new system were concerned with a comparison of the achievable temperatures in a bosonic 174Yb MOT and a fermionic 171Yb MOT. In earlier measurements that were performed in the stationary apparatus using a frequency-doubled Ti:Sapphire laser we had observed temperatures in the fermionic MOT well below the Doppler

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limit of 690 µK, which were attributed to effective polarization gradient cooling which is possible for fermionic atoms with nuclear spin but not for bosonic isotopes. The study that was performed in the new apparatus yielded significantly higher temperatures with around 10 mK for 174Yb and 6 mK for 171Yb. We attribute these high temperatures mainly to the much larger atom number as compared to our previous study where the number of fermionic 171Yb atoms was only several 105. These findings rule out efficient direct loading of the optical lattice from a precooling MOT of fermionic ytterbium due to the limited lattice depth (on the order of 100 µK). 2.1.3 Performed tests and results: Test and optimization of pre-cooling of Yb using improved diode laser setup A new all-diode-laser based setup for precooling of Yb including the operation of a Zeeman slower was implemented in the existing apparatus as well as in the new compact apparatus. With this method up to 3 x 107 atoms (for 174Yb) could be loaded into a precooling MOT at a temperature of several mK within several hundred ms. These values meet the required standards for an optical lattice clock with Yb. Optimization and characterization of polarization gradient cooling of fermionic 171Yb and 173Yb in the pre-cooling stage Initial studies of polarization cooling in the fermionic isotopes in a low-atom number MOT (using a frequency-doubled Ti:Sapphire laser) suggested that it might be possible to load the magic-wavelength optical lattice directly from a pre-cooling MOT (@399 nm). Our recently performed tests at higher atom numbers using a diode laser system for the precooling MOT indicate that the low temperatures are incompatible with the required atom numbers. Optimization and characterization of post-cooling We have tested two alternative approaches for postcooling. By optimizing the parameters of the postcooling MOT (@ 556 nm) we have achieved temperatures below 40 µK at a density of 1011 atoms/cm-3 which meets the requirements for loading of the optical lattice and therefore operation of a Yb optical lattice clock. In addition, we have realized a scheme in which the post-cooling MOT is directly loaded from the Zeeman slower, thus circumventing the need for a pre-cooling MOT. While this scheme is well-suited for initial spectroscopic investigations of the Yb clock transition it is not appropriate for the ultimate operation of an Yb optical clock due to the long loading time of more than 10s. Comparison of cooling schemes The tests we have performed show that the two-stage cooling scheme with a precooling MOT operating at 399 nm (using diode lasers) and the postcooling MOT operating at 556 nm is the most appropriate for the operation of an optical lattice clock with Yb. A portable laser system for the postcooling using a frequency-doubled diode laser is currently being developed.

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Workpackage 2.2 - Ytterbium trap-laser and optical lattice setup (HHUD-I) This workpackage is concerned with the development of an optical lattice for ultracold Yb atoms including the required laser system. Optical lattices are essentially standing waves of light. If the wavelength is red-detuned with respect to the dominant atomic resonance, microtraps for atoms are formed in the antinodes of the optical standing wave. Depending on the number of sumperimposed standing waves optical lattices can be realized in 1D, 2D or 3D. In an optical lattice clock, the optical lattice has to be operated at a so-called magic wavelength which minimizes perturbations of the optical clock transition. For Yb, the magic wavelength has been determined to be 759 nm [Barber2006]. Within this workpackage we have developed a diode laser system at 759 nm with an output power of up to 1W and a setup for a 3D optical lattice for bosonic atoms which includes a power build-up resonator inside the vacuum chamber with a power enhancement of around 100. 2.2.1 High-power diode laser system at 759 nm The main options for generating the required radiation at 759 nm at a power level of 1W are Ti:Sapphire lasers or diode-laser based systems. The main advantage of a Ti:Sapphire laser is its inherent frequency stability and spectral purity while its drawback is the need for a high power pump laser. Since the use of a high power pump laser would eventually be in conflict with the goal to realize a compact, low-power, transportable system, we have chosen to set up a diode-laser based system which is significantly more compact and consumes only a fraction of the electrical power required for operation of a Ti:Sapphire laser. The standard approach for a diode-laser based system would be the amplification of a grating-stabilized diode laser in a so-called tapered amplifier. In contrast our system is making use of a single self-injected tapered diode laser which has its own grating for stabilization. The self-injected tapered laser, shown in Fig. 2.2.1, generates a power of up to 600 mW at a laser diode current of 2.5 A, which is well below the maximum allowed current of 3 A. We have chosen this operating condition in order to ensure a long lifetime of the diode laser. Since the spatial mode of the tapered laser is not a pure TEM00 mode, only about 50% of the laser output can be coupled into a fiber and consecutively used for the optical lattice. Nevertheless, if the laser is used together with the enhancement cavity described in the next section, the achieved power level is sufficient for the creation of an optical lattice for Yb atoms. For the application of the self-injected diode laser as a light source for an optical lattice for ultracold atoms, the spectral properties play a crucial role. The first requirement is that the laser linewidth is smaller than the linewidth of the enhancement cavity in order to be able to couple light efficiently into the latter. Fig.2.2.2. shows a spectrum of the enhancement cavity taken with the self-injected diode laser. We have observed a linewidth of 2.4 MHz, which is thus an upper limit for the linewidth of the laser. Presumably, the laser linewidth is even narrower, since the observed linewidth can be fully explained by the known mirror reflectivities of the cavity.

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Fig. 2.2.1.: Setup for the self-injected tapered diode laser for the optical lattice at 759 nm, showing the optical grating in the center of the picture. The diode chip is located in the middle of the copper holder on the right.

Fig. 2.2.2.: Spectrum of the enhancement cavity (free-specatral range 750 MHz) taken with the self-injected diode laser (left). The width of a resonance line (right) is 2.4 MHz, dominated by the cavity linewidth due to the finite mirror reflectivities.

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2.2.2 Robust setup for a 3D optical lattice for bosonic atoms The requirements for the optical lattice in an Yb optical lattice clock are that the potential depth is sufficient to hold an atomic ensemble prepared in a postcooling MOT (i.e. the potential depth is to be on the order of several 10 µK) and that the spatial extent of the optical lattice is sufficiently large in order to ensure good spatial overlap with the postcooling MOT (i.e. the waist of the laser beams is to be larger than 100 µm). For a one dimensional standing wave created by a retroreflected laser beam at the magic wavelength of 759 nm these requirements can be fulfilled with a beam waist of 150 µm and a laser power of 30 W. Under these conditions the individual optical microtraps inside the standing wave have a depth of 80 µK. Since the maximum usable power that can be obtained from our diode laser system is on the order of 300 mW (after taking into account losses in optical elements and due to mode cleaning), our lattice design requires an enhancement cavity with a finesse around 300 and a corresponding enhancement factor of approx. 100 (see Fig. 2.2.2). The cavity is to be fully contained in the vacuum chamber, in order to avoid the intracavity losses due to optical elements such as vacuum viewports which would otherwise reduce the enhancement factor. We have modified the basic linear geometry of the enhancement cavity by introducing five folding mirrors in the cavity, to create an intersection of three orthogonal standing waves inside the resonator where a 3D optical lattice is formed (see Fig. 2.2.3). Thanks to interference between the three standing waves the resulting trap depth in the 3D lattice will be several 100 µK.

Fig. 2.2.3.: Alignment of the laser beam in the folded enhancement cavity. The laser beams with a wavelength of 759 nm are made visible by imaging the light scattered from water vapour onto an IR-sensitive CCD-camera The 3D trap will be located at the intersection of the three beams.

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The setup for the enhancement resonator includes a stable support structure made out of invar, a special steel with a low thermal expansion coefficient. The resonator length is 24 cm and there are no adjustable parts inside the resonator. The support structure is glued together using a vacuum compatible ceramic glue which is also used to attach the mirrors. In order to set up the resonator geometry in such a way that an intersection of three standing waves in the center is realized, the beam path inside the resonator is constantly monitored during construction of the resonator using the high-power laser diode with a wavelength of 759 nm. This is achieved by diffusion of water vapour into the resonator and observation of the laser light which is scattered from the vapour. Simultaneously, the cavity finesse is monitored in order to ensure efficient coupling of light into the resonator. With this procedure we have been able to set up a resonator with a finesse close to 300 and overlap of the three standing waves at the intersection point. After the enhancement resonator is aligned and all parts are glued together, it is placed inside the vacuum chamber (see Fig. 2.2.4.).

Fig.2.2.4: Folded enhancement resonator mounted inside a vacuum chamber. The chamber has an inner diameter of 8 cm. The vacuum chamber used here is an exact copy of the vacuum chamber which is used in the compact clock apparatus. As upcoming activities, the enhancement resonator for the optical lattice will be inserted into the vacuum system of the optical clock apparatus. First tests on loading of the optical lattice are planned until the end of the year. The lattice is primarily suited for an investigation of the optical clock transition in bosonic Yb [Barber2006], since the spatially varying polarization in the 3D lattice would result in perturbations of the optical clock transition in fermionic Yb. 2.2.3 Performed tests and results: Test of Yb trap laser frequency stability The linewidth of the high-power diode laser has been measured to be below 3 MHz (which is the current resolution of our test setup). Observed drifts on the order of several 10 MHz/min can be easily corrected by stabilizing the laser to an optical cavity. Optical filtering methods will be applied to filter broad band noise out of the laser spectrum if required.

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Workpackage 2.3 - Ytterbium clock laser (HHUD-I)

2.3.1 Development of a compact laser system for a clock laser 2.3.1.1 Introduction

Single-mode external cavity grating stabilized diode lasers (ECDL) are well established for a wide variety of applications, including as clock lasers. However, some spectral ranges are impossible or difficult to reach because of material limitations. For example, the occurrence of strain-induced dislocations in InGaAs quantum well lasers limits the longest lasing wavelength to approx. 1.1 µm. For this reason, for this workpackage in the proposal we had suggested the use of a 1156 nm fiber laser instead. The low output power later specified by the manufacturer (few mW on a “best effort” basis) would have meant a potentially insufficient power at 578 nm. Therefore, a first alternative was implemented, sum-frequency generation of a Nd:YAG laser (1064 nm) and a diode laser (1267 nm), which was reported in the 1st year project status report (September 2007). More recently, a new approach has become possible, InGaAs quantum dot (QD) lasers. These lasers are filling the gap between 1100 nm and 1300 nm. In particular, the wavelength range covered by their second-harmonic radiation lies in the yellow. The reduction from a pair of lasers to a single laser is a significant simplification inasmuch also the frequency conversion subsystem is simplified: in case of resonant conversion, the lock system is simpler as well. When we initiated our work on the QD lasers, the state-of-the-art was at a very early stage [Tierno07]. We implemented a QD laser in the external cavity Littrow configuration and demonstrated for the first time, that these lasers are in principle suitable for high-resolution experiments, with linewidth well below the 100 kHz level. The work is described in full detail in [Nevsky08]. 2.3.1.2 Basic properties of the quantum dot laser

The QD laser chip exhibits a normal output facet and 5°- tilted rear facet, both anti-reflection coated with a residual reflectivity of ~ 0.5%. The gain chips are mounted p-side up on the AlN carriers. The schematic of the QD-ECDL is shown in Fig. 2.3.1. The radiation emitted from the tilted facet (angle of 17° with respect to the normal to the waveguide) is collimated with an AR coated aspheric lens. A diffraction grating reflects the first diffraction order back to the laser chip, forming a Littrow-like configuration. Coarse wavelength tuning of the laser is obtained by changing the incidence angle of the grating. For fine tuning of the laser frequency a piezo transducer (PZT) that displaces the grating is used, allowing a mode-hope-free tuning range of about 3 GHz. The output radiation of the laser is also collimated by an aspheric lens and corrected by an AR coated prism pair, forming an almost square cross-section beam of size approx. 6 x 6 mm. The whole construction including the laser chip, objectives and the grating is mounted on a copper plate, the temperature of which is stabilized with Peltier elements to better than 1 mK. The laser is driven by a custom made ultra-low noise current source (max output current 750 mA) with a residual RMS current noise on the order of 1 µA. The typical output power of the laser at the wavelength 1156 nm was 130 mW at the max output current.

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Fig.2.3.1 Schematic of the external cavity quantum dot laser. In this setup (“low-noise” implementation) the laser wavelength could be changed in the range from approx. 1148 nm to 1250 nm just by tilting the grating. Under proper alignment of the reflection grating the sidemode suppression was measured to be more than 35 dB within the whole emission range. Using operating currents above 750 mA, a tuning range exceeding 200 nm as well as an output power of more than 500 mW at a central wavelength of about 1180 nm has been achieved, still keeping single spatial mode. 2.3.1.3 Spectral properties

The free-running linewidth of the QD-ECDL was measured by producing the heterodyne beat between two almost identical laser systems, tuned to 1165 nm, and is shown in Fig. 2.3.2. The beat was detected with a high-bandwidth photodetector and analyzed with a spectrum analyzer. The observed beat linewidth of 280 kHz (on a timescale of several 10 µs) implies a linewidth of about 200 kHz for a single laser. In order to perform a detailed analysis of the laser frequency noise, in particular of the intrinsic linewidth, we used an external ring cavity (the cavity later used for doubling) as a frequency discriminator. The laser wave reflected from the cavity was detected by a fast photo-detector and demodulated using a double-balanced RF mixer. The cavity was locked to the laser using the PZT of the cavity mirror. The servo bandwidth was several kHz, nevertheless providing a stable lock over several hours. The frequency fluctuations of the laser were analyzed from the closed loop error signal at the output of the frequency mixer. The bandwidth of this signal was about 7 MHz. For frequencies above the locking bandwidth (approx. 10 kHz), the fluctuations correspond to those of the unlocked (unstabilized) laser. The frequency noise was characterized for two distinct QD-ECDL configurations, having resonator lengths of 32 mm and 115 mm, respectively, from the grating to the output AR facet of the laser chip. The larger resonator length showed a reduced sensitivity of the laser frequency to the operating current (30 MHz/mA in comparison to 100 MHz/mA for the 32 mm resonator). This also led to a factor 9 reduction of the frequency noise level. A simple explanation for this is the reduced influence of the optical path length fluctuations occurring in the laser chip when the total cavity length increases. The estimated laser linewidth is about 180 kHz and 60 kHz for the short and long resonators, respectively, ignoring the effect of low-frequency instability of the laser frequency, caused by mechanical instability of the laser resonator, mains pick-up and other similar parasitic effects, which effectively result in a larger linewidth. Thus, the longer resonator was used in the following.

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-5 0 5

0,0

0,5

1,0

beat

note

pow

er (a

.u.)

Frequency (MHz)

FWHM 280 kHz

Fig. 2.3.2 Power spectrum of the beat note between two free-running QD-ECDLs (cavity lengths approx. 35 mm). The spectrum analyser resolution bandwidth is 30 kHz.

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2.3.2 Clock laser pre-stabilization and operation 2.3.2.1 Implementation In order to reduce the laser linewidth and frequency drift, frequency stabilization to a reference cavity was implemented, shown in Fig. 2.3.3. As a reference cavity we used a SiO2 Fabry-Perot resonator that has previously been used for relativity experiments at 1064 nm. The resonator consists of a 30 mm long SiO2 cylinder with a diameter of 25 mm and two high-finesse mirrors, optically contacted to its end faces. At the wavelength of 1156 nm the finesse of the cavity is about 10 000. This cavity was used for initial developments because its relatively large linewidth simplified frequency-locking of the laser. The cavity is placed inside a vacuum chamber and temperature stabilized with a Peltier element to better than 1 mK. The temperature sensitivity of the cavity was measured to be about 100 MHz/K (thermal expansion coefficient 3.8 x 10-7/K). After the two optical isolators (OI), a part of the beam is split off with an acousto-optic frequency shifter (AOM) and coupled to the reference cavity. The AOM is used in double pass, and the light diffracted twice (and shifted by twice the AOM frequency) is sent to the reference cavity. The laser radiation reflected from the cavity is detected with a low-noise photodetector. The Pound-Drever-Hall error signal is obtained in the standard way. A PID type servo system controls the laser diode current. The bandwidth of the lock is about 500 kHz with a 1/f roll-off at low frequencies. A stable lock of the laser to the cavity was obtained (see below). The double-pass AOM approach doubles the frequency scan range and prevents changes of the beam direction. When the AOM frequency is changed by tuning a synthesizer, the frequency of the light reaching the cavity also changes, but the lock changes the laser frequency such that the cavity resonance is maintained. Thus, the wave undiffracted by the AOM (transmitted beam through AOM in Fig. 2.3.3), which contains most of the laser power, is tuned by the negative of the AOM detuning. This stabilized and tuneable 1156 nm radiation is sent to the frequency comb for frequency measurement and is also frequency doubled in a second-harmonic generation (SHG) enhancement cavity and then sent via fiber to the laboratory containing the cold Ytterbium apparatus. The frequency instability of the QD-ECDL locked to the SiO2 cavity was measured using the femtosecond frequency comb (Menlo Systems, FC 8004). The comb is stabilized to an active hydrogen maser (Vremya-Ch) and GPS. The comb is based on the Ti-Sa femtosecond laser (Femtosource Scientific 200) with a repetition rate of 200 MHz. The spectrum of the laser is broadened in the photonic crystal fibre (Crystal Fibre, Femtowhite 800) to 1.5 octave, covering the range from 500 nm to 1500 nm. The heterodyne beat-note between the femtosecond comb and the laser was detected with a low-noise photodetector and measured by means of a dead time free frequency counter. The frequency measurement indicated a relatively large linear drift (30 Hz/s) of the laser frequency, which is probably due to the residual temperature instability of the SiO2 resonator. The Allan deviation of the laser frequency is presented in Fig. 2.3.4. An Allan deviation below 200 Hz is reached for integration times between 2 and 20 s. The estimated linewidth of the prestabilized radiation is 1 kHz.

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MOT

Enhancement cavity

+- Lock

Lock +-

578 nm

OI

PP-LiNbO3

PZTQD-ECDL1156 nm

DC currentmodulation input

Osc. fm=14 MHz

Bias-TRF mixer

RF mixer

AOM

QWP

Frequency comb

350 m to Yb laboratory

ν/2

ν/2

ν/2

ν

F1

F2

F3

F

ν/2+2νsynth

QWP

Synth. νsynth

PD

PD

ω

I(ω)

fluorescencesignal

MOT

Prestabilization cavity

MOT

Enhancement cavity

+- Lock

+- Lock

Lock +-Lock +-

578 nm

OI

PP-LiNbO3

PZTQD-ECDL1156 nm

DC currentmodulation input

Osc. fm=14 MHz

Bias-TRF mixer

RF mixer

AOM

QWP

Frequency comb

350 m to Yb laboratory

ν/2

ν/2

ν/2

ν

F1

F2

F3

F

ν/2+2νsynth

QWP

Synth. νsynth

PD

PD

ω

I(ω)

fluorescencesignal

MOT

Prestabilization cavity

QD-ECDL

prestabilizationcavity

OI

OI

AOM

QWP

PD

pump

to freq. comb

to SHG-cavity

QWP

90 cm

90 cm F2

F3

F1

QD-ECDL

prestabilizationcavity

OI

OI

AOM

QWP

PD

pump

to freq. comb

to SHG-cavity

QWP

90 cm

90 cm F2

F3

F1

Fig. 2.3.3 Schematic and photograph of the clock laser system. OI – optical isolator, Lock: electronic frequency stabilization system. The dimensions of the breadboard are 90 x 90 cm.

89

1 10 100102

1030 100 200 300 400 500

-1

0

1

2

Bea

t-no

te [

kHz]

Time [s]A

llan

devi

atio

n σ y(τ

) [H

z]

Integration time (s)

Fig.2.3.4 Allan deviation of the frequency of the QD-ECDL pre-stabilized to the SiO2 cavity. A linear drift of about 30 Hz/s is removed before calculating the deviation. Inset: typical beat signal time series after subtracting the linear drift, acquisition time 1 s. 2.3.2.2 Second harmonic generation Second harmonic generation (SHG) is performed in an external enhancement cavity containing a periodically poled LiNbO3 crystal (PPLN). The fundamental wave of the QD-ECDL is resonantly enhanced in the ring cavity. The finesse of the cavity is about 200. The PPLN crystal is 25 mm long, 0.5 mm thick and possesses a grating period of 8.33 µm. The crystal end faces are coated at the fundamental and harmonic wavelengths. To prevent optical damage or photorefractive effects, the PPLN crystal is operated in a small oven. At a temperature of about 190°C phase matching for doubling of 1156 nm radiation occurs. The thermal tuning coefficient of the phase-matched fundamental wavelength is 1.15 nm /K. The laser radiation is mode-matched to the cavity using a single focusing lens. A coupling efficiency of ~ 50% is obtained, due to non-perfect laser beam shape and non-optimized input coupler mirror. The two isolators OI transmitted only a fraction of the diode light, resulting in about 32 mW available before the enhancement cavity. Further attempts to increase the incident power by adjusting the optical isolators led to an increased feedback and, as a result, to an unstable lock of the cavity. The power of the generated second-harmonic wave as a function of the incident power follows closely a quadratic dependence, with a maximum of 3.2 mW output at 578 nm, with 32 mW fundamental input power. 2.3.3 Development of a high-finesse reference cavity for reaching 1 Hz linewidth

In order to reach the milestone of 1 Hz clock laser linewidth and 10-15 relative frequency instability, the prestabilized radiation must be further stabilized. To this end, a state-of-the-art reference cavity will be employed. The reference ULE cavity (Fig. 2.3.5) is 10 cm long and is specified with a finesse of about 400 000 at 578 nm. We measured a finesse of 330 000 (4.5 kHz linewidth). The shape of the cavity was analyzed at NIST and UNIFI/LENS with FEM with respect to vibrational sensitivity of its length. The residual sensitivity is estimated to be on the

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order of several 10 kHz/g when appropriately mounted. The cavity is placed in a compact vacuum chamber with a dual-layer temperature stabilization system.

Fig. 2.3.5 Left: ULE reference cavity for 578 nm. Middle: cavity mounted into vacuum and thermal housing. Right: cross sectional view of system. The outer enclosure (vacuum chamber) is made of aluminium and has dimensions of 170 x 108 x 106 mm3. The vacuum in the system (3 x 10-8 mbar) is maintained by a miniature 3-litre ion-getter pump, mounted on top of the aluminium vacuum chamber. To improve thermal radiation shielding and reduce thermal gradients, the reference cavity is placed inside a massive copper box, coated with a thin layer of gold. The copper box is mounted on 4 Peltier (TEC) elements (30x30 mm) which are used for its temperature stabilization and, as a result, for stabilisation of the temperature of the reference cavity. The aluminium vacuum chamber is also placed on the 6 TEC elements (40x40 mm) to provide a second stage of the temperature stabilisation of the ULE cavity. The time constant of the ULE cavity in the vacuum chamber is t ≈ 6 hours and was measured by comparing the shift of a cavity mode frequency at 532 nm with respect to a hyperfine-structure line in molecular iodine upon a temperature change of the aluminium enclosure. The large time constant indicates a good passive isolation of the cavity. In the same way, the coefficient of thermal expansion of the ULE cavity was measured as a function of the temperature. The desired zero CTE occurs near room temperature, at approx. 20.1 °C, a temperature that can be easily maintained in the vacuum chamber with small power consumption.

A low-noise temperature read-out and control system for the cavity environment was developed. Over more than 5 days of continuous measurement no observable temperature drift within a 1 mK measurement error was detected, in spite of a permanent ongoing experimental activity in the laboratory. The residual temperature fluctuations of the inner copper box are shown in Fig. 2.3.6. The temperature instability is below a few mK on timescales above 20 s, which should ensure a very low temperature-induced cavity drift.

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10 100 1000 10000 100000

10-5

10-4

σy(τ) (K)

τ [s]

Fig. 2.3.6 Residual temperature instability of the copper box containing the ULE reference cavity. Shown is the root Allan variance of the temperature sensor signal. Note that this signals contains also the noise of the read-out system, so the shown instability is an upper limit to the actual temperature instability. 2.3.4 Outlook Currently, the optimum approach for stabilization of the 1156 nm laser to the high-finesse ULE cavity is being investigated. A commercial active vibration isolation system has been tested and is ready for use. As a further improvement of the performance of the clock laser system in terms of a compact design as well as a simplified operation it is planned to replace the enhancement cavity by a PPLN waveguide (see also Sec. 2.1.2.3). The waveguide should allow obtaining several mW at 578 nm with a single pass of the fundamental wave through the waveguide.

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Workpackage 2.4 - Yb clock component integration and characterization (HHUD-I, HHUD-II) This workpackage is joint between the group HHUD- I and HHUD-II.

2.4.1. Optical fiber link between clock laser and cold Ytterbium source The frequency metrology laboratory of team HHUD-I, containing the frequency comb and the clock laser, is separated by about 100 m from the Ytterbium laboratory operated by team HHUD-II. We deployed two optical fibers and three electrical cables to link the two above-mentioned laboratories. One fiber is for delivery of the subharmonic of the clock radiation, the other for the clock laser light itself (578 nm). One of the three electrical cables is a special rf cable with low sensitivity. For reasons of fire safety, the optical fibers and electrical cables could not be installed along the shortest path but had to go via the cellar. This included two sections between laboratory level and cellar level, and a cellar crossing between the relevant parts of the building. Thereby the length of the connections reached 350 m. In contrast to the transmission of rf signals through high-frequency cables, laser light passing an optical fiber suffers a spectral broadening of up to several ten Hz/m [Ma94, Pang92, Foreman07], due to variations of the optical path length caused by thermal, mechanical and acoustic perturbations. Measurements on our fiber link (Fig. 2.4.1) indicate a linewidth increase by about 180 Hz.

Figure 2.4.1: Spectral broadening by a 350 m optical fiber. Beat note from a laser wave and its “copy” running back and forth through the fiber. The fiber stabilisation was off. The beat note width is 360 Hz for a double-pass, and would be 180 Hz at the far end of the fiber. The beat note is at 100 MHz and was mixed down to 5 kHz for this measurement.

To cancel out the phase noise induced by fiber perturbations, we employ a simple active stabilisation scheme shown in figure 2.4.2, similar to the scheme described by Ma et al. [Ma94]. This scheme compensates the fiber perturbations by changing the frequency (and thus also the phase) of the laser light entering the fiber so as to offset the following phase perturbations. The scheme is similar to the one described in Sec. 1.6.4, but is here implemented with bulk optical components. Refer to figure 2.4.2 for the abbreviations that follow below.

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Figure 2.4.2: Fiber stabilisation scheme. HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarising beam splitter; GP: (BK-7) glass plate; M: mirror; FC: fiber collimator; PD: photo detector; LO: local oscillator, MX: mixer; F: loop filter; VCO: voltage control oscillator; AOM: acoustic optical modulator; G: driver for the AOM.

In this scheme a fraction of the laser light propagated through the fiber is back-reflected from the fiber output at GP to the fiber input side and is compared with the “original” laser wave at the fiber input (at PD). In detail, the setup works as follows: The polarisation of the laser light is adjusted such that a small fraction is refracted by the PBS to the PD. This is the “original” laser wave. Meanwhile, the larger part passes the PBS and is circular-polarized by a QWP. After that, the light is diffracted by an AOM, driven at a frequency close to 50 MHz and imparting a phase φ, and is coupled into the optical fiber. The fiber is a single mode, non-polarisation maintaining fiber. At the end of the fiber, about 4% is back reflected through the fiber by a wedged glass plate GP. Due to the circular polarisation of the laser light, perturbations in both polarisations are picked up, and we assume a similar effect is produced by the fiber on both. The back reflected light passes the AOM and the QWP in the opposite direction and is linear-polarized in order to be deflected by the PBS. For obtaining the beat note with the original wave, the back-reflected light passes a QWP twice on its way to the PD. Due to the double pass through the AOM, the beat note frequency is twice the AOM frequency (100 MHz), plus frequency fluctuations induced by the fiber. In a frequency mixer the beat-note is compared to a 100 MHz signal (LO) of an H-maser stabilized frequency generator using a mixer. The output of the mixer is low-pass filtered and represents the error signal. The AOM is driven by a VCO that is controlled by the error signal. The error signal is filtered by a PLL loop filter with an open loop unity gain frequency of 20 kHz. The servo bandwidth amounts to 30 kHz. For analysis of the performance of the fiber noise compensation system we used 1064 nm light from a stable Nd-YAG laser with a linewidth of 1 kHz on a 100 ms time scale. Figure 2.4.3 shows the power spectral density of the 100 MHz beat note between the original wave before the fiber and the back reflected wave, measured on the photodiode PD. The compensation system was operating.

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Figure 2.4.3: Power spectral density of the rf signal produced by the beat between the probe beam before the fiber and the back reflected beam, measured on the photodiode PD. The spectrum was composed from eight individual measurements of different resolution bandwidth, shown in colour. Central narrow peak at 100 MHz is the carrier. The fractional power contained in the carrier is 93.3 %. Servo bumps arising from the PLL lock system occur at approximately 25 kHz around the carrier. Inset: close-in of the carrier, showing the noise pedestal.

The sharp and strong central peak in the spectrum indicates that the PLL is working properly. While the linewidth of the carrier cannot be resolved, it is certainly smaller than 1 Hz. An accurate spectrum was obtained from eight measurements taken with different resolution bandwidth with an Agilent E4440A spectrum analyzer. The spectrum data allowed to determine the fractional power contained in the carrier, defined by [Prevedelli94]

( ) ( )2 cP exp ,P( )d

+∞

−∞

η = = − φν ν∫

,

Here cP is the power in the carrier at 100 MHz and )(P ν is the power spectral density, shown in

Figure 2.4.3. This expression holds when 12 <<ϕ . We found 0 9332.η = , implying a root-mean-square (rms)-phase error of mrad. 263=rmsϕ The bumps around the carrier indicate a servo bandwidth of 25 kHz, consistent with the calculated servo bandwidth. In the unlocked case the beat note is broadened to about 360 Hz (see Figure 2.4.1).

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In Figure 2.4.4 the Allan deviation of the beat note is shown. The black line represents the case when noise is uncompensated (lock is off) while the blue line is for the case when it is compensated. At 1 s gate time the Allan deviation is 0.19 Hz, confirming the stability grade also obtained above by calculating the phase error. The value for the uncompensated case is one order of magnitude higher at this integration time, and does not vary significantly with averaging time. In the locked case we observe a τ-1/2 - variation of the root variance. A small peak is seen on the time scale of the laboratory temperature variations, which have approximately 1 K amplitude. These variations have some influence because several ten meter fiber lengths and the analog lock electronics are located in the laboratory and are exposed to them. In these measurements, the power used was 2 mW. We have also recorded the phase slips of the beat note. The record shows a phase offset increasing with an average rate of 2π per 40 s, and in addition phase slips relative to this average. This indicates a slight imperfection of the phase lock. However, the resulting frequency offset is only 10 mHz.

Figure 2.4.4: Allan deviation (root Allan variance) of the beat note between the probe beam at the input and the light back reflected through the fiber, in lock (blue) and free running (black). τ is the integration time.

In conclusion, the implemented fiber link allows a frequency resolution of 50 mHz over 10 s integration time, and a linewidth less than 1 Hz. In the upcoming studies, the fiber link will be operated at the relevant Yb wavelengths 1156 or 578 nm, where we expect similar performance. This performance is compatible with the milestones for the stability and accuracy of the Yb clock.

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2.4.2 Observation of the clock transition in fermionic 171Yb The interrogation of the 171Yb clock transition at 578 nm was performed in a directly loaded postcooling MOT (see Sec. 2.1.), using the frequency-doubled light from the QD-ECDL clock laser system as described in section 2.3, which is connected to the MOT via a fiber link. In this first measurement, the fiber stabilization, described in section 2.4.1., was not used since the passive frequency stability of the fiber was good enough for an initial characterization of the clock transition. As mentioned, the spectroscopy is performed in a directly loaded precooling MOT operating on the 1S0 → 3P1 transition of Yb. The MOT temperature as measured by a time-of-flight technique is around 100 µK. If the MOT is not exposed to the clock laser, the number of atoms in the MOT reaches a steady-state value within roughly 10 s, which is determined by a dynamic equilibrium between the loading rate into the MOT and the loss rate which is mainly due to collisions (light-assisted and background). The number of atoms in the MOT can be easily monitored by observing the fluorescence of the atoms due to the interaction with the cooling light. If clock laser light resonant with the 1S0 → 3P0 at 578 nm is introduced, additional losses occur since atoms can then be transferred into the long-lived metastable 3P0 state which is no longer trapped in the MOT. This process in turn leads to a reduction of the steady-state value of the fluorescence which depends on the clock-laser frequency. The fluorescence intensity is observed by a photomultiplier and converted into a voltage signal. Scanning of the laser frequency occurred by means of the AOM in the clock laser setup (Fig. 2.3.3) in discrete steps. The measurement cycle is controlled by a PC via LabVIEW and works as follows. First, the laser is tuned to within a few 100 kHz near the expected transition frequency via a wavemeter. In the following loop, the PC first reads the beat note frequency between the 1156 nm laser light and the H-maser referenced frequency comb and calculates the optical frequency. The beat note is filtered by a tracking-oscillator and counted by a dead time free frequency counter with a gate time of 1 s.

Figure 2.4.1: Observation of the 1S0 → 3P0 clock transition at 578 nm. Fluorescence arising from the 556 nm 1S0 → 3P1 cooling light during interrogation of the clock transition. The observed transition frequency is shifted by approx 0.3 MHz and broadened to 736 kHz due to systematic

97

effects in the MOT.

Subsequently the voltage from the fluorescence observing photomultiplier at the MOT is read out by the PC. In the next step the AOM frequency is changed via a signal generator for the next measuring point. Here the corresponding frequency step appears by a factor of four in the interrogation light, due to the AOM double pass and the SHG. All frequencies and voltage levels are logged to a data file before the next cycle starts. We scanned the AOM frequency in the loop several times over a total range of 700 kHz back and forth with a step size of 2 kHz.

The result of one scan is shown in Figure 2.4.1. The observed transition line is shifted by approx. 0.31 MHz to higher frequency due to light shift of the clock levels by the 556 nm cooling light and is broadened to 736 kHz FWHM, due to a combination of Doppler broadening and saturation broadening in the MOT.

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C Planning of activities in the second half of the project SYRTE WP 1.1 Sr clock physics package optimization

- AM noise reduction on the 2nd generation lattice. This will be done by stabilisation to a Fabry-Perot cavity. Completion of this task is a prerequisite for operating the second lattice clock and perform the measurements with 10-16 or better resolution -Measurements of lattice induced frequency shifts. The main targeted effect is the tensorial frequency shift. We'll also perform experiments to observe the lattice shift due to E2 and M1 couplings that was recently pointed out by Taichenachev et al. (PRL 101, 193601 (2008)), or at least put an upper limit on this effect. All in all, this will allow completing the determination of optimal lattice parameters as initially planned.

WP 1.6 Sr clock characterization

- Implementation of the temperature stabilisation and completion of the tests of the new ultra-stable cavity. Comparison of the two Sr clocks with this new laser as a clock laser. The goal is to reach 10-15τ-1/2.

- Measurement of systematic effects with 10-16 accuracy. In addition to lattice induced shifts which are part of WP1.1, this includes all the effects discussed in §1.6.3 except the blackbody radiation shift for the evaluation of which a significant modification of the vacuum chamber would be necessary.

PTB WP 1.2 Sr clock physics package optimization II - We will investigate 2D lattice configurations to avoid the collisional shifts that have been

observed both in 88Sr and spin polarized 87Sr. With the typical atom numbers of less than 106, already in 2D lattices there will be less than one atom per potential well.

- Interrogation methods using Rabi and Ramsey techniques will be compared concerning accuracy and signal to noise ratio.

WP 1.5 Sr clock laser - The transportable clock laser replacement cavity will be finished and tested. LENS WP 1.3 Strontium Pre-cooling laser

‐ Further optimization of the pre-cooling laser with test on compact breadboard for producing frequencies (until February 2009)

‐ Ultimate the assembling and test of compact breadboard for MOT frequencies production (until February 2009)

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WP 1.4 Transportable cold Strontium source

‐ Completion of the transportable Strontium source and realization of an electronic control system compatible for two-stage cooling of Sr and for spectroscopy on clock transition (until August 2009)

‐ Integration of the transportable system with pre-cooling laser and first test on first stage cooled atoms (until September 2009)

‐ Test on the transportable cold Strontium source at PTB (to be discussed further, see next section LENS-PTB test )

Proposed LENS-PTB Test: As an extension of WP 1.4.2 we propose to move the Sr compact setup to PTB for spectroscopy on cold atoms in a lattice, to be performed during the last two months of the project (end of 2009). LENS can provide the electronic control system for the apparatus (computer controlled temporized TTLs and analog output channels) PTB can provide all the additional lasers for the second stage cooling, the clock laser and the lattice laser. All lasers are fiber coupled to be easily connected to the LENS setup, As PTB is using the funds for personnel, it is mostly the time that is required for the preparation and the measurements (3 months), which would delay or stop other investigations. Most easily PTB could give up the investigations (WP 1.2) on multidimensional lattices, that are also carried out for Yb and detailed investigations of detection schemes that are already performed at SYRTE and the clock laser comparison in Düsseldorf (WP 3). PTB needs some additional equipment such as fibers, fiber couplers and flipping mirrors (5 k€). At the midterm meeting (October 2008) LENS proposed a compact fiber coupling system. The system costs ca. 40 k€ (fibers, fiber splitter, fiber collimators). This system is necessary in order to make the Sr compact setup compatible for the two-stage cooling of Sr with an easy interface with the PTB red laser. Under discussion is a purchase of the fiber coupling system by PTB, but loaned to LENS for the duration of the preparation (in Florence) and at the end of SOC returned to PTB LENS needs support for travel and living expenses in PTB for one/two person for at least two months (10 k€) HHUD-I WP 2.3 Yb clock laser:

- Realization of compact clock laser setup with nonresonant frequency doubling, stabilized to ULE cavity (until February 2009)

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- Characterization of the short-term instability and long-term drift of the clock laser (until June 2009)

WP 3 Clock laser comparison:

- Phase lock of frequency comb to Yb clock laser (until June 2009) - Characterization of the long-term drift of the clock laser (until June 2009) - Transport of PTB’s Sr clock laser to Düsseldorf for a comparison with the Yb laser: if the

LENS-PTB experiments are performed this item may not be implementable due to time constraints

HHUD-II WP 2.1 Cold Ytterbium Source:

‐ Realization of “green” postcooling MOT using a dye laser (until December 2008)

‐ Realization of “green” postcooling MOT using a frequency doubled diode laser (until February 2009)

‐ Characterization of “green” postcooling MOT and full characterization of cold Yb source incompact clock apparatus completed (until April 2009)

WP 2.2 Optical lattice: ‐ Loading of atoms into optical lattice (until January 2009)

‐ Characterization of the loading scheme of the optical lattice (until April 2009)

‐ Further optimization of optical lattice setup for 1D and 3D optical lattice (until October 2009)

WP 2.4 Ytterbium clock component integration and characterization (together with HHUD-I)

‐ Test of spectroscopy of the optical clock transition in a MOT of fermionic Yb in the new compact apparatus (until April 2009)

‐ Spectroscopy on the optical clock transition in an optical lattice (until June 2009)

‐ Characterization of the optical clock transition in Yb in an optical lattice at the magic wavelength (until December 2009 and beyond)

WP 3 Clock laser comparisons

- Transport of PTB’s Sr clock laser to Düsseldorf for a comparison with the Yb laser: if the LENS-PTB experiments are performed this item may not be implementable due to time constraints

WP 4 Synthesis of results (until January 2010, after completion of WP 1.4.2)

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