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 S (f)=100 Hz 2 /Hz for 1 mHz 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 I 2 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 LISA detectivity ~ 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. Doing better: cold atoms

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

4. Detection N at ~2  10 9  r ~  mm T ~1  K ΔV ~2 cm.s -1 V launch ~ 4m.s -1 H ~1m T ~500ms T c ~0.8-2s Selection 3 2 1 Atomic fountains: Principle of operation

5. transition probability P NO AVERAGING ONE POINT = ONE MEASUREMENT OF P Ramsey fringes in atomic fountain Fluctuations of the transition probability: 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. FO2 frequency stability This stability is close to the quantum limit. A resolution of 10 -16 is obtained after 6 hours of integration. With Cs the frequency shift is then close to 10 -13 ! With a cryogenic sapphire oscillator, low noise microwave synthesis (~ 3  10 -15 @ 1s) Frequency stability with a cryogenic Oscillator

7. Fountain Accuracy Fountain (LNE-SYRTE)FO2(Cs) second order Zeeman1920.4 (0.1) Blackbody radiation-168.7 (0.6) Collisions + cavity pulling-129.3 (1.3) Residual Doppler effect0.0 (3.0) Recoil0.0 (1.4) Neighbouring transitions.0.0 (0.1) Microwave leaks, spectral purity, synchronous perturbations. 0.0 (0.5) Collisions with residual gaz.0.0 (0.5) Total3.8 EffectShift and uncertainty (10 -16 )

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

9. Optical frequency standards ? Frequency stability : Increase (x 10 5 ) Frequency accuracy: most of the shifts (expressed in absolute values) don't depend on the frequency of the transition (Collisions, Zeeman...). Three major difficulties -Ability to compare frequencies (no fast enough electronics ) -Recoil and first order Doppler effect -Interrogation oscillator noise conversion (Dick effect). Optical fountain at the quantum limit !!!!!!!!! The best optical clocks so far exhibit frequency stabilities in the 10 -15  -1/2 range together with an accuracy around 10 -14.

10. Doppler Effect Atomic fountains limited to ~ 10 -16 Calcium optical clock ~ 10 -15 v Room temperature atoms: v ~ 300 m/s Doppler shift ~ 10 -6 Cold atoms: v ~ 1 m/s Standing wave in a cavity Q ~10 4 Symmetry of the interrogation = 0 Residual Doppler shift ~ 10 -16 Can the Doppler frequency shift be decreased down to ~ 10 -18 ???? Doppler shift is given by k. v, independant on n 0 in fractional units

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

12. Doppler/recoil, trapped particles 2-level atom: coupling: Trapped atoms : eigenstates of H ext are more and more localized (delocalized) in real (momentum) space as  t increases. is not an eigenstate of H ext, 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 Laser 1 Laser 2 Tight enough confinement implies shifts of the levels by tens of kHz: 10 kHz ~ several 10 -11 of an optical frequency laser intensity (E 2 ) and polarization are difficult to control at a « metrological » level. Relevant parameter is the difference between both clock levels shit. /2 atoms

14. 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) Clock transition 1 S 0 - 3 P 0 transition (  =1mHz) Atoms confined in an optical lattice. Light shift cancellation at the magic wavelength of the lattice. Similar scheme with Yb, Hg, Mg, Ca… 1S01S0 3D13D1 3S13S1 1P11P1 3P03P0 698 nm Transition horloge (~1 mHz) 461 nm 2.56 µm 679 nm 87 Sr

15. 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) Experimental setup

16. Longitudinal temperature given by sidebands ratio T z = 2 µK, 95 % of the atoms in |n z =0> 1S01S0 n z =0 3 2 1 Ground state Excited state 3P03P0 n z =0 3 2 1 Longitudinal sidebands frequency depends on the transverse excitation. Shape of sidebands gives the transverse temperature. T r = 10 µK Optical lattice clocks: state of the art 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). M. Boyd et al. Science 314, 1430 (2006) Line-Q is four orders of magnitude larger than in an atomic fountain, highest line-Q ever obtained for any form of coherent spectroscopy.

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. Differential light shift cancellation ?  Feasibility is conditioned by the magnitude of higher order effects = > Scale as E 4  U 0 2  Higher order terms : Hyperpolarisability  Neutral atoms in an optical lattice :  At the magic wavelength, the first order term cancels  U 0 =10 E r (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 A. Brusch et al. PRL 96, 103003 (2006)  Experimentally demonstrated to be negligible for 10 -18 accuracy (SYRTE,Sr)  Actual control of the trap shift at a level of 10 -7

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)