1. 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 - 10 th, 2008 87-Strontium Optical Lattice Clock with high Accuracy and Stability

2. 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 10  Decrease τ by 100 Clock Stability (Allan Deviation) Clock Accuracy Reduce environmental Effects (EM Fields)

3. 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 Source Sub-Hz width Δ ν/ν~ 1x10 -15 @ 1s Drift < 1 Hz/s Insensitive to vibration RBW 333 mHz FWHM ~400 mHz ~330 mHz FWHM 2.1 Hz g

4. Optical Lattice Clock A Strontium-87 Optical Lattice Clock 689 nm  ~ 7.4 kHz Cooling 698 nm Clock Transition 87 Sr (I=9/2)  ~ 1 mHz 461 nm,  ~ 32 MHz Cooling (5s 2 ) 1 S 0 F=9/2 F=11/2 (5s5p) 1 P 1 F=7/2 F=9/2 3P13P1 3P03P0 F=11/2 F=7/2 F=9/2 Ultra-narrow 1 S 0 - 3 P 0 clock transition Neutral atoms give large S/N Can be laser cooled to 1  K. 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 Hz N = 10 6  10 -18 @ 1 s Loftus et al., Phys. Rev. Lett. 93, 073003 (2004).

5. Spectroscopy at the Magic Wavelength 1-D Lamb-Dicke Regime 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, … 1S01S0 3P03P0

6. m F = -9/2m F = +9/2  Lock to spin-polarized sample  1st order Zeeman shift cancelled  Vector (axial) light shift cancelled  Tensor light shift absorbed into λ m Lock to Spin Polarized Samples mFmF photon scatter 3P13P1 3P03P0 3P23P2 1S01S0 π-polarized, F=9/2→F’=7/2 population

7. Clock Comparison: NIST Ca Clock 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

8. AC Stark shiftDensity ShiftZeeman 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

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

10. Density 1x10 11 /cm 3 p-wave, Temp-dependent Fermionic collisions (under investigation) s-wave, not identical inhomogen. excitation ? Collisions with Identical Fermions?

11. Collisions of “almost” Identical Fermions P-wave threshold ~ 30 mK, i.e., only S-P contribution: Temperature dependent Density 1x10 11 /cm 3

12. Collisions of “almost” Identical Fermions P-wave threshold ~ 30 mK, i.e., only S-P contribution:

13. Collisions of “almost” Identical Fermions P-wave threshold ~ 30 mK, i.e., only S-P contribution:

14. Inhomogeneous Excitation temperature

15. 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

16. Decreasing the Density Shift  Preliminary results: More homogeneous excitation  Lower density shift!

17. 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!!!

18. Sr Frequency Variation over 2.5 yr Linear Drift Sinusoidal amplitude Ye, JILA Lemonde, LNE-SYRTE Katori, Univ. Tokyo  constrains linear drift of fundamental constants  constrains coupling coefficients to gravitational potential

19. Sr Frequency Variation over 2.5 yr Linear Drift Ye, JILA Lemonde, LNE-SYRTE Katori, Univ. Tokyo  constrains linear drift of fundamental constants

20. Constraints on Gravitational Coupling Tests linear model: Sr: JILA, SYRTE, U. Tokyo Hg + : NIST H-Maser: NIST V. V. Flambaum, Int. J. Mod. Phys. A 22, 4937 (2007) Blatt et al., PRL 100, 140801 (2008)

21. Acknowledgments Absolute Frequency Measurement S. Diddams T. Heavner L. Hollberg S. Jefferts T. Parker J. Levine Optical Carrier Transfer S. Foreman J. Bergquist S. Diddams J. Stalnaker Optical evaluation of Sr Z. Barber S. Diddams T. Fortier L. Hollberg N. D. Lemke C. Oates N. Poli J. Stalnaker Ultracold Collisions K. Gibble S. Kokkelmans P. Julienne P. Naidon

22. m F = -9/2m F = +9/2  Lock to spin-polarized sample  1st order Zeeman shift cancelled  Vector (axial) light shift cancelled  Tensor light shift absorbed into λ m Pushing Forward: Spin Polarized Samples mFmF photon scatter 3P13P1 3P03P0 3P23P2 1S01S0 π-polarized, F=9/2→F’=7/2 population

23. Controlling the Density Shift

24. Uncertainty Evaluation: Optical Comparison not listed: residual 1 st order Doppler, DC Stark Ludlow et al., Fortier et al. Science 319, 1805 (2008), Campbell et al., atom-ph/0804.4509v1 submitted to Metrologia

25. Non-Zero collision Shift Shift: -8.9(0.9)x10 -15  0 =1 x 10 11 cm -3 Small collision shift possibly due to spectator atoms m F = -9/2m F = +9/2

26. Optical Clock Constraints on Linear Drifts Linear Fit to gives H/Cs: MPQ Sr/Cs: JILA, SYRTE, U. Tokyo Yb + /Cs: PTB Hg + /Cs: NIST Blatt et al., PRL 100, 140801 (2008) (Al + /Hg + : NIST)