Atomic Clocks

Physical Seminar- Quantum Optics and Nanophotonics -

Peter Deiml 20.05.2014

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Table of contents

• Why do we need an exact definition of time?

• Current time standard

• Spectroscopy

• Ramsey-Spectroscopy

• Caesium beam clock

• (Laser Cooling)

• Caesium fountain clock

• Outlook: Optical Clock

3Quantum Optics and Nanophotonics Atomic Clocks Peter Deiml

Why do we need an exact definition of time? [Bauch, 2003],[Bauch, 2012]

“The accurate measurement of time and frequency is vital to the success of many fields of science and technology.” [Bauch, 2003]

Some scientific examples:

• Other SI-units (e.g. meter)

based upon the second

• Spectrum of atoms (QM,QED)

• „Proof“ of equivalence principle,

SR, GR (Hafele-Keating-/ Maryland-

experiment)

• Gravitational waves

• Fine structure constant

constant?

Some everyday examples:

• Global Positioning System

(GPS)

• Telecommunication

• Supply of energy

Fig. 2: NAVSTAR satellite [Wiki GPS, 2014]Fig. 1: Hafele, Keating

& stewardess aboard airplane with two atomic clocks [Wiki HKE, 2014]

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Definition of the second (1967)„The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom“ [BIPD, 2006]

Quantum Optics and Nanophotonics Atomic Clocks Peter Deiml

• Why exactly 9192631770 periods of the radiation?

• Why atomic properties?

• Why the Cs-133 atom?

• Why hyperfine levels?

Current time standard

→ value equals to ephimerises second Fig. 3: Solar system with sun and the nine planets (not true to scale) [SeaSky, 2014]

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Why atomic properties? [Bauch, 2012]

Current time standard

„ Zeit [ist] die Stellung des kleinen Zeigers meiner Uhr “ [Einstein, 1905]

Fig. 4: Spacetime in special relativity [Wiki SR, 2014]

• Every frame of reference has its own time

Time determined by natural constants!

• Atomic properties determined by natural constants (in rest frame of the atom)

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Current time standard

Why the Cs-133 atom? [PTB]

• Technology for measuring the resonance frequency was available in 1967

• Small thermal velocity due to large mass (later: Doppler effect → 0)

• Only two hyperfine levels in the ground state

• The only natural isotope of caesium

• Small boiling point (670°C)

• Transition has small natural line width

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Why hyperfine levels? [Audoin et al., 2005] Current time standard

Quantum number configuration of the outermost

electron of Cs-133:

Fig. 6: Cutting of the hyperfine structure of Cs-133[Bauch, 2003]

• No fine structure (J)

• Transition for time standard: F = 3 ↔ F = 4

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SpectroscopyGeneral ideaInvestigation of the answer of atoms or molecules to a laserbeam

Examples:

• Information about structure of stars Fig. 8: Dispersion of white light by a prism [Wiki SpC, 2014]

Fig. 7: UVES on the very large telescope on Cerro Paranal (Chile)[Wiki SpC, 2014]

• Scientific applications: medicine (MRT),

chemistry, biology

Perfect method for measurement of the second

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Doppler effect:

Natural line width:

Fig. 9: spectrum of low-pressure mecury bulb[Wiki NLW, 2014]

Fig. 10:Gauß-Voigt profile with underlying natural line width[Meschede, 2007]

SpectroscopyBroadening mechanisms [Meschede, 2007]

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SpectroscopyBroadening mechanisms [Meschede, 2007]

Fig. 11: Scheme of spectroscopy experiment[Wiki TOF, 2014]

Other broadening mechanisms [Audoin et al., 2006]

Time-of-flight (TOF) broadening [Meschede, 2007]

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Ramsey-Spectroscopy

Young‘s double slit (Position space):

Fig. 12: Scheme of Young‘s double slit [Wiki YDS, 2014] Fig. 13: Distribution of intensity [Wiki YDS,2014]

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Ramsey-Spectroscopy

Fig. 14: Scheme of Ramsey-spectroscopy

Fig. 15: See frame 11

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Caesium beam clockCaesium beam tube [Bauch, 2003],[Audoin et al., 2006]

Fig. 16: Scheme of the magnetically deflected caesium beam tube [Bauch, 2003]

• Analyzer deflects F = 4 atoms towards detector

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Caesium beam clockThe CS2 clock at the Physikalisch Technische Bundesanstalt (PTB)

Fig. 17 : Vertical section of the vacuum chamber of PTB‘s primary clock CS2[Bauch, 2003]

Fig. 18: See frame 13

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Caesium beam clockFunction of Polarizer/Analyzer [Audoin et al., 2006]

Fig. 19: Energy of the hyperfine levels via the magentic flux density [Audoin et al., 2006]

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Caesium beam clockC field inside the cavity [Riehle, 2004]

Fig. 20: See frame 12

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Caesium beam clockFrequency response of a caesium beam tube [Audoin et al., 2006]

Fig. 21: Scheme of the resonance of the central part [Bauch, 2003]

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Caesium beam clockFrequency response of a caesium beam tube [Audoin et al., 2006]

Fig. 22: See frame 17

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Laser cooling [Weyers et al., 1999]

Fig. 23: Order of laser beams, their polarisation in an optical molasse [Weyers et al., 1999]

Fig. 24: Order of laser beams, their polarisation in a magneto-optical trap [Weyers et al., 1999]

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Caesium fountain clock

General structure [Weyers et al., 1999]

Fig. 25: Simplified setup of the atomic fountain clock [Wynands et al., 2005]

• Only one interaction zone is needed

• State-selection, Ramsey cavity and C-field analogeously to caesium beam clock

• Different detection method with lasers

• Difference: Preparation of F = 4 atoms

• Charge of magneto-optical trap

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Caesium fountain clocksResults of caesium fountain clock [Weyers et al., 1999]

Fountain clocks more precise than beam clocks

Figure 21 (CSF1):

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Outlook

Optical clocks

Fig. 27: Temporal development of frequency uncertainty [Udem et al.,2009]

Optical clocks need the frequency comb technology

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Take-home messageCurrent time standard:

• Exact definition is needed

• Definition of the second & its justification

Spectroscopy:

• Method for realization of time standard

• Broadening mechanisms

Caesium beam/fountain clock:

• General setup

• Functional principle and task of all

components

• Frequency response signal

• Fountain clock more precise than beam clock

Optical clocks:

• More precise than caesium clocks

• Frequency comb technology is nessecary

Ramsey-Spectroscopy:

• Double slit in time space

• Strong analogy to Young‘s double slit in

position space

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Thank you for your attention

and

feel free to ask questions!(after the next presentation )

Hallo

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AppendixDetection and measurement of transition [Weyers et al., 1999]

Fig. 20: Scheme of the detection zone [Weyers et al., 1999]

• Measurement of flourescence by two detectors (photodiodes)

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References

[Audoin et al., 2006] Audoin C., Guinot B., The measurement of time, Cambridge University Press, 2001

[Bauch, 2003 ] Bauch A., Caesium Atomic Clocks: Function, Performance and Applications, Measurement Science and Technology 14, 1159-1173 (2003)

[Bauch, 2012] Bauch A., Zeitmessung in der PTB, PTB Mitteilungen 122, 2012[Bauch et al., 1998] Bauch A., Fischer B., Heindorff T., Schröder R., Performance of the PTB reconstructed

primary clock CS1 and an estimate of ist current uncertainty, Metrologia 35, 829-845, 1998[BIPD, 2006] Bureau international des poids et mesures, Organisation interfouvernementale de la

Convention du Mètre. Le Système international d‘unités, 8e édtion, 2006[Demtröder, 2005] Demtröder, W., Experimentalphysik 3, Atome, Moleküle und Festkörper, 3. Auflage,

Springer Verlag, Berlin, Heidelberg, New York, 2005[Einstein, 1905] Einstein A., Zur Elektrodynamik bewegter Körper, Annalen der Physik und Chemie. 17, S.

891 – 921, 1905[Fließbach, 2006] Fließbach T., Allgemeine Relativitätstheorie, Spektrum, 2006[Meschede, 2007] Meschede D., Optics, Light and Lasers, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim,

2007[PTB 1] Physikalisch-Technische Bundesanstalt, Wie funktioniert eine Atomuhr?

[PTB 2] Physikalisch-Technische Bundesanstalt, Optische Atomuhren

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References

[Riehle, 2004] Riehle F. Frequency Standards: Basics and Applications, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2006

[Udem et al., 2009] Udem T., Holzwarth R., Hänsch T. W., Femtosecond optical frequency combs, European Journal of Physics – Special Topis 172,69-79, 2009

[Weyers et al., 1999] Weyers S., Griebsch D., Hübner U., Schröder R., Tamm C., Bauch A., Die neue Caesiumfontäne der PTB, PTB-Mitteilungen 109, 483-491, 1999

[Wynands et al., 2005] Wynands R., Weyers S., Atomic fountain clocks, Metrologia 42, 64-79, 2005

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Web references[Wiki SR, 2014] http://en.wikipedia.org/wiki/Special_relativity, 02.05.2014[Wiki GPS, 2014] http://de.wikipedia.org/wiki/Global_Positioning_System, 02.05.2014[Wiki SC, 2014] http://de.wikipedia.org/wiki/Bahnhofsuhr, 02.05.2014[Wiki MBD, 2014] http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution, 02.05.2014[Wiki SpC, 2014] http://en.wikipedia.org/wiki/Spectroscopy, 02.05.2014[Wiki NLW, 2014] http://de.wikipedia.org/wiki/Linienbreite, 02.05.2014[Wiki TOF, 2014] http://de.wikipedia.org/wiki/Flugzeitverbreiterung, 02.05.2014[Wiki YDS, 2014] http://de.wikipedia.org/wiki/Doppelspaltexperiment, 09.05.2014[SeaSky, 2014] http://www.seasky.org/solar-system/solar-system.html, 18.05.2014[Spiegel, 2013]http://www.spiegel.de/wissenschaft/technik/zeitmessung-physiker-bauen-zuverlaessigste-uhr-aller-zeiten-a-917409.html, 18.05.2014