Jan W. Thomsen, G. K. Campbell, A. D. Ludlow, S. Blatt, M. Swallows,

1. 87-Strontium Optical Lattice Clock with high Accuracy and Stability http://jilawww.colorado.edu/YeLabs From Quantum to Cosmos July 6 - 10th, 2008 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

2. Q = ν/Δν Feedback (accuracy) Δν ν Ultrastable laser Atom(s) Clock Accuracy Reduce environmental Effects (EM Fields) Optical comb Optical Clock Components Clock Stability (Allan Deviation) Increase Q or S/N by 10 Decrease τ by 100 Diddams et al., Science 293, 825 (2001). Ye et al., Phys. Rev. Lett. 87, 270801 (2001).

3. Stable Local Oscillator: Sub Hz Lasers ~330 mHz RBW 333 mHz 8 cm FWHM ~400 mHz Diode Source Sub-Hz width Δν/ν~1x10-15 @ 1s Drift < 1 Hz/s Insensitive to vibration g FWHM 2.1 Hz Boyd et al. Science 314, 1430-1433 (2006) Ludlow et al., Opt. Lett. 32, 641 (2007)

4. F=7/2 (5s5p) 1P1 F=7/2 F=11/2 F=9/2 F=9/2 3P1 F=11/2 689 nm g ~ 7.4 kHz Cooling 461 nm, g ~ 32 MHz Cooling F=9/2 3P0 698 nm Clock Transition 87Sr (I=9/2) g ~ 1 mHz (5s2) 1S0 F=9/2 A Strontium-87 Optical Lattice Clock Optical Lattice Clock • Ultra-narrow 1S0-3P0 clock transition • Neutral atoms give large S/N • Can be laser cooled to 1mK. • 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 = 106 10-18 @ 1 s Loftus et al., Phys. Rev. Lett. 93, 073003 (2004).

5. Spectroscopy at the Magic Wavelength 1-D Lamb-Dicke Regime 3P0 1S0 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, …

6. mF = -9/2 mF = +9/2 Lock to Spin Polarized Samples population photonscatter mF 3P2 3P1 3P0 π-polarized, F=9/2→F’=7/2 • Lock to spin-polarized sample • 1st order Zeeman shift cancelled • Vector (axial) light shift cancelled • Tensor light shift absorbed into λm 1S0

7. Clock Comparison: NIST Ca Clock Ludlow et al., Science 319, 1805 (2008) Foreman et al., Rev. Sci. Instr. 78, 021101 (2007) Foreman et al., PRL 99, 153601 (2007) 3 x 10-16 @ 200 s All optical comparison allows rapid evaluation

8. Uncertainty Evaluation: Optical Comparison Density Shift Zeeman Shift AC Stark 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.

9. 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

10. Density 1x1011/cm3 Fermionic collisions (under investigation) ? s-wave, not identical inhomogen. excitation p-wave, Temp-dependent Collisions with Identical Fermions?

11. Collisions of “almost” Identical Fermions P-wave threshold ~ 30 mK, i.e., only S-P contribution: Density 1x1011/cm3 Temperature dependent

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) n0: 429,228,004,229,800 Hz Last two JILA points agree to better than 5x10-16 Last JILA and Paris points agree to better than 5x10-16 Coming Soon : PTB, NPL, LENS, NICT… Sr Clock now accepted as secondary standard by BIPM!!!

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

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

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

22. mF = -9/2 mF = +9/2 Pushing Forward: Spin Polarized Samples population photonscatter mF 3P2 3P1 3P0 • Lock to spin-polarized sample • 1st order Zeeman shift cancelled • Vector (axial) light shift cancelled • Tensor light shift absorbed into λm π-polarized, F=9/2→F’=7/2 1S0

23. Controlling the Density Shift

24. 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

25. Non-Zero collision Shift mF = -9/2 mF = +9/2 Shift: -8.9(0.9)x10-15 r0=1 x 1011cm-3 Small collision shift possibly due to spectator atoms

26. (Al+/Hg+: NIST) 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)