Jan W. Thomsen, G. K. Campbell, A. D. Ludlow, S. Blatt, M. Swallows, T. Zelevinsky, M. M. Boyd, M. Martin, T. Nicholson and J. Ye

JILA, NIST and University of Colorado

$ Funding $

ONR, NSF, AFOSR, NASA, DOE, NIST

http://jilawww.colorado.edu/YeLabs

From Quantum to Cosmos July 6 - 10th, 2008

87-Strontium Optical Lattice Clock with high Accuracy and Stability

Feedback(accuracy)

Optical Clock Components

Optical comb

Ultrastable laser

Q = ν/Δν

Δν

ν

Atom(s)

Diddams et al., Science 293, 825 (2001).Ye et al., Phys. Rev. Lett. 87, 270801 (2001).

Increase Q or S/N by 10Decrease τ by 100

111

0

NSQ

noise

Clock Stability(Allan Deviation)

Clock AccuracyReduce environmental Effects (EM Fields)

8 cm

Boyd et al. Science 314, 1430-1433 (2006) Ludlow et al., Opt. Lett. 32, 641 (2007)

Stable Local Oscillator: Sub Hz Lasers

Diode SourceSub-Hz width

Δν/ν~1x10-15 @ 1sDrift < 1 Hz/s

Insensitive to vibration

-15 -10 -5 0 5 100.0

0.2

0.4

0.6

0.8

1.0

Sig

nal (

arb.

lin.

uni

ts)

Frequency (Hz)

RBW333 mHz

FWHM~400 mHz

~330 mHz

FWHM 2.1 Hz

g

Optical Lattice ClockA Strontium-87 Optical Lattice Clock

689 nm ~ 7.4 kHz

Cooling

698 nm Clock Transition

87Sr (I=9/2) ~ 1 mHz

461 nm, ~ 32 MHz

Cooling

(5s2) 1S0

F=9/2

F=11/2

(5s5p) 1P1F=7/2

F=9/2 3P1

3P0

F=9/2

F=11/2

F=7/2

F=9/2

•Ultra-narrow 1S0-3P0 clock transition•Neutral atoms give large S/N•Can be laser cooled to 1K.• All transitions accessible with diode lasers•Field insensitive states• Weak two-body atom interaction expected – small density shift•Accessible magic wavelength (813 nm)

Stability Estimate

Δν = 1 HzN = 106

10-18 @ 1 s

Loftus et al., Phys. Rev. Lett. 93, 073003 (2004).

Spectroscopy at the Magic Wavelength

trapclock

traprecoil

1-D Lamb-Dicke Regime

3.0~/0 zrecoilkx

Ye et al. PRL 83, 4987 (1999)Katori et al. PRL 91, 173005 (2003) Ludlow et al., PRL 96, 033003 (2006) Sr, Yb, Ca, Mg, Hg, …

trap

1S0

3P0

mF = -9/2 mF = +9/2

Lock to spin-polarized sample 1st order Zeeman shift cancelled Vector (axial) light shift cancelled Tensor light shift absorbed into λm

Lock to Spin Polarized Samples

mFphotonscatter

3P13P0

3P2

1S0

π-polarized, F=9/2→F’=7/2

pop

ula

tion

Clock Comparison: NIST Ca Clock

1 10 10010-16

10-15

10-14

10-13

Sr vs. NIST Maser Sr vs. NIST Ca

Alla

n D

evia

tion

Time (s)

3 x 10-16 @ 200 s

Ludlow et al., Science 319, 1805 (2008)

Foreman et al., Rev. Sci. Instr. 78, 021101 (2007)Foreman et al., PRL 99, 153601 (2007)

All optical comparison allows rapid evaluation

AC Stark shift Density Shift Zeeman Shift

To measure the systematic, the parameter of interest is varied every 100s.

Many pairs of data are then used to calculate the resulting shift and average down the final uncertainty.

Uncertainty Evaluation: Optical Comparison

Uncertainty Evaluation: Optical Comparison

not listed: residual 1st order Doppler, DC Stark

Ludlow et al., Fortier et al. Science 319, 1805 (2008),Campbell et al., atom-ph/0804.4509v1 submitted to Metrologia

21

29

23

25

27

21

29

23

25

27

21

272

92

52

3

21

272

9

25

23

01S

03P Density 1x1011/cm3

p-wave,Temp-dependent

Fermionic collisions (under investigation)

s-wave, not identicalinhomogen. excitation

?

Collisions with Identical Fermions?

Collisions of “almost” Identical Fermions

P-wave threshold ~ 30 K, i.e., only S-P contribution:

Temperature dependent

Density 1x1011/cm3

Collisions of “almost” Identical Fermions

P-wave threshold ~ 30 K, i.e., only S-P contribution:

Collisions of “almost” Identical Fermions

P-wave threshold ~ 30 K, i.e., only S-P contribution:

Inhomogeneous Excitation

temperature

Controlling the Density Shift

Inhomogeneity: large number of

motional states occupied by the atoms.

Measured by looking at the dephasing of Rabi oscillations.

As the temperature of the atomic cloud is decreased, a smaller number of motional states are occupied, leading to better contrast in the Rabi oscillations

Decreasing the Density Shift

Preliminary results:

More homogeneous excitation Lower density shift!

50

60

70

80

90

Tokyo Boulder Paris

Sr-

0 (H

z)International Effort (Sr vs. Cs)

0: 429,228,004,229,800 Hz

Coming Soon : PTB, NPL, LENS, NICT…

Last two JILA points agree to better than 5x10-16

Last JILA and Paris points agree to better than 5x10-16

Sr Clock now accepted as secondary standard by BIPM!!!

72

74

76

78

Sr-

0 (H

z)

Sr Frequency Variation over 2.5 yr

Linear Drift

Sinusoidal amplitude

Ye, JILALemonde, LNE-SYRTEKatori, Univ. Tokyo

constrains linear drift of fundamental constants

constrains coupling coefficients to gravitational potential

Sr Frequency Variation over 2.5 yr

Linear Drift

Ye, JILALemonde, LNE-SYRTEKatori, Univ. Tokyo

constrains linear drift of fundamental constants

Constraints on Gravitational Coupling

Tests linear model:

Sr: JILA, SYRTE, U. TokyoHg+: NISTH-Maser: NIST

V. V. Flambaum, Int. J. Mod. Phys. A 22, 4937 (2007)Blatt et al., PRL 100, 140801 (2008)

Acknowledgments

Absolute Frequency Measurement S. DiddamsT. HeavnerL. HollbergS. JeffertsT. ParkerJ. Levine

Optical Carrier Transfer S. ForemanJ. BergquistS. DiddamsJ. Stalnaker

Optical evaluation of Sr Z. Barber

S. DiddamsT. Fortier

L. HollbergN. D. Lemke

C. OatesN. Poli

J. Stalnaker Ultracold CollisionsK. Gibble

S. KokkelmansP. JulienneP. Naidon

mF = -9/2 mF = +9/2

Lock to spin-polarized sample 1st order Zeeman shift cancelled Vector (axial) light shift cancelled Tensor light shift absorbed into λm

Pushing Forward: Spin Polarized Samples

mFphotonscatter

3P13P0

3P2

1S0

π-polarized, F=9/2→F’=7/2

pop

ula

tion

Controlling the Density Shift

Uncertainty Evaluation: Optical Comparison

not listed: residual 1st order Doppler, DC StarkLudlow et al., Fortier et al. Science 319, 1805 (2008),Campbell et al., atom-ph/0804.4509v1 submitted to Metrologia

-0.5 0.0 0.5 1.0 1.5 2.0 2.50

5

10

15

20

25

30

35

40

Occ

urr

en

ces

Freq Shift (Hz/0)

21

29

23

25

27

21

29

23

25

27

21

272

92

52

3

21

272

9

25

23

01S

03P

Non-Zero collision Shift

Shift: -8.9(0.9)x10-15

0=1 x 1011cm-3

Small collision shift possibly due to spectator atoms

mF = -9/2 mF = +9/2

Optical Clock Constraints on Linear Drifts

Linear Fit to

gives

H/Cs: MPQSr/Cs: JILA, SYRTE,

U. TokyoYb+/Cs: PTBHg+/Cs: NIST

Blatt et al., PRL 100, 140801 (2008)

(Al+/Hg+: NIST)