Des horloges atomiques pour LISA ?

1. Des horloges atomiques pour LISA ? Pierre Lemonde Bureau National de Métrologie – SYRTE (UMR CNRS 8630) Observatoire de Paris, France Journées LISA-FRANCE Annecy, Janvier 2007

2. LISA frequency noise cancellation LISAdetectivity~ 50 µrad for averaging times between 10 and 1000 s. TDI => cancellation of the laser frequency (phase) noise by an appropriate combination of measured beatnotes. Sn(f)=100 Hz2/Hz for 1 mHz < f < 1 Hz => required rejection is ~140 dB @ 10-2 Hz Stabilisation to a high finesse cavity, limited by thermal motion of the cavity mirrors Stabilisation to atomic or molecular resonances: -microwave clocks (fountains) -optical clocks (molecules, ions, neutral atoms) Nd:YAG stabilisation to a I2 transition J. Ye et al. Phys. Rev. Lett.. 87,270801 (2001) ~ 4 10-14 t-1/2 down to 4 10-15 @ 1000 s Flicker floor about 4 10-15 Doingbetter: cold atoms

3. atomic resonance macroscopic oscillator correction atoms interrogation Stability of a laser stabilized to atomic resonances Short term frequency stability: atomic quality factor Long term frequency stability: control of systematic effects. 10-15@1s=> 3 10-18@1000 s. + transition should be insensitive to external perturbations

4. Nat~2109 r~1.5-3mm T ~1mK ΔV ~2 cm.s-1 Vlaunch ~ 4m.s-1 H ~1m T ~500ms Tc ~0.8-2s Atomic fountains: Principle of operation Selection 3 2 1 Detection

5. Fluctuations of the transition probability: Ramsey fringes in atomic fountain transition probability P NO AVERAGING ONE POINT = ONE MEASUREMENT OF P We alternate measurements on bothe sides of the central fringe to generate an error signal, which is used to servo-control the microwave source

6. Frequency stability with a cryogenic Oscillator With a cryogenic sapphire oscillator, low noise microwave synthesis (~ 310-15 @ 1s) FO2 frequency stability This stability is close to the quantum limit. A resolution of 10-16is obtained after 6 hours of integration. With Cs the frequency shift is then close to 10-13!

7. Fountain Accuracy Effect Shift and uncertainty (10-16)

8. atomic resonance macroscopic oscillator correction atoms interrogation Going further: Two possible ways atomic quality factor -as high as possible + transition should be insensitive to external perturbations -low natural width -Fourier limit, long interaction time -low oscillator spectral width Atomic transition in the optical domain A clock in space -Large atom number -low noise detection scheme -low noise oscillator

9. Optical frequency standards ? Frequency stability : Increase(x 105) !!!!!!!!! Optical fountain at the quantum limit Frequency accuracy: most of the shifts (expressed in absolute values) don't depend on the frequency of the transition (Collisions, Zeeman...). -Ability to compare frequencies (no fast enough electronics ) -Recoil and first order Doppler effect -Interrogation oscillator noise conversion (Dick effect). Three major difficulties The best optical clocks so far exhibit frequency stabilities in the 10-15t-1/2 range together with an accuracy around 10-14.

10. v Doppler Effect Doppler shift is given by k.v, independant on n0 in fractional units Room temperature atoms: v ~ 300 m/s Doppler shift ~ 10-6 Cold atoms: v ~ 1 m/s Standing wave in a cavity Q ~104 Symmetry of the interrogation <v> = 0 Residual Doppler shift ~ 10-16 Atomic fountains limited to ~ 10-16 Calcium optical clock ~ 10-15 Can the Doppler frequency shift be decreased down to ~ 10-18 ????

11. 2-level atom: Free atoms : eigenstates of Hext have a well defined momentum (plane waves) E acts on internal and external degrees of freedom coupling: is the translation operator by hks in momentum space Ee Ef p Doppler/recoil, quantum picture resonance frequency shift recoil Doppler

12. coupling: Doppler/recoil, trapped particles 2-level atom: eigenstates of Hext are more and more localized (delocalized) in real (momentum) space as wt increases. Trapped atoms : is not an eigenstate of Hext, however in the tight confinement regime « Strong carrier » surrounded by « small » detuned motional sidebands Lamb-Dicke confinement, no more problem with motional effects External potential has to be exactly the same for both clocks states

13. Tight confinement of atoms atoms Laser 2 Laser 1 l/2 Tight enough confinement implies shifts of the levels by tens of kHz: 10 kHz ~ several 10-11 of an optical frequency laser intensity (E2) and polarization are difficult to control at a « metrological » level. Relevant parameter is the difference between both clock levels shit.

14. 87Sr 3S1 679 nm 1P1 3D1 461 nm 2.56 µm 3P0 698 nm Transition horloge (~1 mHz) 1S0 An optical clock with trapped atoms Katori, Proc. 6th Symp. Freq. Standards and Metrology (2002) Pal’chikov, Domnin and Novoselov J. Opt. B. 5 (2003) S131 Katori et al. PRL 91, 173005 (2003) Atoms confined in an optical lattice. Light shift cancellation at the magic wavelength of the lattice. Similar scheme with Yb, Hg, Mg, Ca… Clock transition 1S0-3P0 transition (G =1mHz)

15. Experimental setup Experiment with Sr (Tokyo, SYRTE, JILA, PTB, Florence, NMIJ, NRC, NSTC, …) Other possibilities Yb (NIST, Washington, Dusseldorf, INRIM, …), Hg (SYRTE, Tokyo), Mg (Hannover, Copenhagen), Ca (PTB, NIST)

16. 3P0 Excited state 3 2 1 nz=0 1S0 3 Ground state 2 1 nz=0 Optical lattice clocks: state of the art Longitudinal temperature given by sidebands ratio Tz = 2 µK, 95 % of the atoms in |nz=0> Longitudinal sidebands frequency depends on the transverse excitation. Shape of sidebands gives the transverse temperature. Tr = 10 µK A. Brusch et al. PRL 96, 103003 (2006)

17. Optical lattice clocks: state of the art Experimental resonance in a Sr optical lattice clock (JILA, Boulder). Line-Q is four orders of magnitude larger than in an atomic fountain, highest line-Q ever obtained for any form of coherent spectroscopy. M. Boyd et al. Science 314, 1430 (2006)

18. Optical lattice clocks: state of the art -3 independent measurements in excellent agreement to within a few 10-15 -Very different trapping deths: 150 kHz to 1.5 MHz: control of differential light shift @ a 10-6 level -still preliminary…

19. Neutral atoms in an optical lattice : • At the magic wavelength, the first order term cancels => ScaleasE4aU02 • Higher order terms : Hyperpolarisability • Feasibility is conditioned by the magnitude of higher order effects Differential light shift cancellation ? • U0=10 Er (36 kHz) is enough to cancel motional frequency shift P. Lemonde, P. Wolf, Phys. Rev. A 72 033409 (2005) Accuracy of 10-18 Control at a level of 10-8 x Light shift • Experimentally demonstrated to be negligible for 10-18 accuracy (SYRTE,Sr) • Actual control of the trap shift at a level of 10-7 A. Brusch et al. PRL 96, 103003 (2006)

20. Optical lattice clocks: milestones -2001: Proposal by H. Katori (U-Tokyo) -2003: Observation and frequency measurement of the clock transition (SYRTE, Sr) accuracy 5 10-11 -2003: Observation of the clock transition in the Lamb-Dicke regime (Tokyo, Sr) linewidh 700 Hz -2005: Accuracy evalation at the level of 5 10-14 (Tokyo, JILA, Sr) -2005: Linewidths below 100 Hz (Tokyo, NIST-Yb). -2005: Experimental demonstration that higher order effects will not limit the clock accuracy (SYRTE) -2005: Extension of the scheme to bosonic isotopes (NIST Yb) -2006: Accuracy approaching 10-15 (SYRTE,JILA), linewidths below 10 Hz (JILA, NIST),… -2006: frequency stability < 10-14 t -1/2 (NIST, JILA) Perspective: stability < 10-16 t-1/2, control of systematics: < 10-17

21. Towards space optical clocks • Main technologies are common to the PHARAO project • optical clocks in space : ESA project (cosmic vision)