Optical clocks, present and future fundamental physics tests Pierre Lemonde LNE-SYRTE

Fractional accuracy of atomic clocks

Systematic effects-accuracy Zeeman effect: Independent on the clock transition frequency Spectral purity, leakage,...: Cold collisions: Neighbouring transitions: Blackbody radiation shift: differential in fountains Cs: 1.7 10-14, Sr, Yb ~ 5 10-15, Hg : 2.4 10-16, Al+ 8 10-18 Doppler effect: Proportional to the clock frequency for free atoms, a trap is required Potential gain 104 Potential gain 104 Potential gain 104 Potential gain 104 Potential gain 102 @ Optical frequencies all these effects seem controllable at 10-18 or better !

Interest of optical clocks Ultimate gain on the frequency stability : 104 Q~4 1014, N~106, Tc ~ 1s Ultimate gain on the frequency accuracy > 102 <10-18 -A « good » clock transition -Ability to control external degrees of freedom. -Ultra-stable lasers Key ingredients Single ion clocks an neutral atom lattice clocks are two possible ways forward

Quantum references: ions or atoms Multipolar couplings: E2, E3 2P1/2 2S1/2 2D3/2 2F7/2 Yb+(PTB, NPL) 369 nm 436 nm 467 nm d=3 Hz d=10-9 Hz Sr+ (NPL,NRC) d=0.4Hz 2S1/2 2P1/2 2D5/2 422 nm 674 nm Other ions: Hg+ (NIST), Ca+(Innsbruck, Osaka, PIIM) Intercombination transitions d=1 mHz 1S0 1P1 3P0 461 nm 698 nm d=8 mHz 1S0 1P1 3P0 167 nm 267 nm Sr (Tokyo, JILA, SYRTE,…), Yb (NIST, INRIM, Tokyo,…) Hg (SYRTE, Tokyo), In+ Al+ (NIST)

Quantum logic clock One logic ion for cooling and detection One clock ion for spectroscopy External degrees of freedom are coupled via Coulomb interaction

Al+ clocks C. Chou et al. Science 329, 1630 (2010) C. Chou et al. PRL 104 070802 (2010)

Al+ clock accuracy budget Ion clock with sub 10-17 accuracy C. Chou et al. PRL 104 070802 (2010)

Neutral atom clocks

Trapping neutral atoms Trapping : dipole force (intense laser) Confinement : standing wave l/2 Optical lattice clocks Trap shifts D> 10-10 reaching 10-18, effect must be controlled to within 10-8

Problems linked to trapping Trap depth : light shift of clock states 3 parameters : polarisation, frequency, intensity Trap depth required to cancel motional effects to within 10-18 : at least 10 Er (i.e. 36 kHz, or 10-11 in fractional units for Sr) Both states are shifted. The differential shift should be considered P. Lemonde, P. Wolf, Phys. Rev. A 72 033409 (2005)

Solution to the trapping problem Polarisation : use J=0  J=0 transition, which is a forbidden by selection rules Intensity : one uses the frequency dependence to cancel the intensity dependence Such a configuration exists for alkaline earths 1S0  3P0 3P0 Sr 1S0 3D1 3S1 1P1 3P0 698 nm 461 nm 2.56 µm 679 nm 1S0 lm : "longueur d'onde magique" M. Takamoto et al, Nature 453, 231 (2005)

Experimental setup

Ultra-narrow resonance

Lattice clock comparison

Trap effects

E2-M1 Effects E1 interaction Traps atoms at the electric field maxima M1 and E2 interactions Creates a potential with a different spatial dependence Le spectré sur une plus grand echelle fait apparaître les bandes laterale motionelle des atomes pieges. What can we do, get temperature Need to enhance Potentiel moyen plus faible pour les atomes avec une haute excitation transverse

E2-M1 Effects E1 interaction Traps atoms at the electric field maxima M1 and E2 interactions Creates a potential with a different spatial dependence This leads to a clock shift Le spectré sur une plus grand echelle fait apparaître les bandes laterale motionelle des atomes pieges. What can we do, get temperature Need to enhance Potentiel moyen plus faible pour les atomes avec une haute excitation transverse

The shift is measured by changing n and the E2-M1 effects Measurements The shift is measured by changing n and the trap depth U0=100-500 Er Le spectré sur une plus grand echelle fait apparaître les bandes laterale motionelle des atomes pieges. What can we do, get temperature Need to enhance Potentiel moyen plus faible pour les atomes avec une haute excitation transverse The effect is not resolved, not a problem Upper bound 10-17 for U0=800 Er

Trap shifts Hyperpolarisability d<1 µHz/Er2 Tensor and vector shift. Fully caracterized and under control <10-17 All known trap effects are well understood and not problematic <10-17 P.G. Westergaard et al., arxiv 1102.1797

87Sr lattice clock accuracy budget A. Ludlow et al. Science, 319, 1805 (2008) Frequency difference between Sr clocks at SYRTE <10-16 10-17 feasible at room temperature. BBR, a quite hard limit. Next step: cryogenic, Hg ?

L. Yi et al., Phys. Rev. Lett. 106, 073005 (2011) Towards a Hg lattice clock First lattice bound spectroscopy of Hg atoms First experimental determination of Hg magic wavelength 362.53 (21) nm L. Yi et al., Phys. Rev. Lett. 106, 073005 (2011)

Optical clocks worldwide Ion clocks NIST (Al+, Hg+), PTB-QUEST (Yb+, Al+), NPL (Yb+, Sr+), Innsbruck (Ca+)… Neutral atom clocks Tokyo (Sr, Hg), JILA (Sr), SYRTE (Sr, Hg), NIST (Yb), PTB (Sr),… Space projects SOC project (ESA – HHUD, PTB, SYRTE, U-Firenze) SOC2 (EU-FP7) Optical clock as an option for STE-QUEST mission Performing fundamental physics tests implies comparing these clocks

Clock comparisons Fiber « Round-trip » method for noise compensation Round-trip noise detection LAB 1 Accumulated Phase noise Ultra-stable 1.542 µm laser Noise correction LAB 2 FP 2FP Link instability measurement Fiber Demonstrated at the 10-19 level over hundreds of km over telecom network Global comparisons = satellite based systems ACES-MWL 2014-2017 down to a few 10-17, L. Cacciapuoti (next talk) Mini-DOLL coherent optical link, K. Djerroud et al. Opt. Lett. 35, 1479 (2009)

Fundamental tests on ground Stability of fundamental constants a/a expected improvement by 2 orders of magnitude 10-18/yr m/m limited by microwave clocks. Possible improvements if nuclear transitions are used. Dependence of a to local gravitational potential Expected improvement by 2 orders of magnitude 10-8 d(GM/rc2) Massive redondancy due to the large number of atomic species/transitions

Optical clocks in space Earth orbit Highly elliptical orbit. x100 improvement on ACES goals Optional optical clock for STE-QUEST mission (pre-selected as M mission in CV2). Solar system probe Outer solar system (SAGAS-like). Further improvement by 2 orders of magnitude on gravitational red-shift and coupling of a to gravity. Probe long range gravity. Inner solar system. Probe GR in high field. S. Schiller et al. Exp. Astron. (2009) 23, 573 P. Wolf et al. Exp. Astron. (2009) 23, 651

Transportable Strontium Source (LENS/U.Firenze)-SOC project main requirements: 1. compact design 2. reliability 3. low power consumption main planning choices: 1. compact breadboard for frequency production 2. all lights fiber delivered 3. custom flange holding MOT coils and oven with 2D cooling optical breadboard 120 cm x 90 cm Schioppo et al, Proc. EFTF (2010) 27

Conclusions Optival clocks with ions and neutrals now clearly outperform microwave standards. Present accuracy and long term stability 10-17 . Where is the limit ? Long distance comparisons techniques are progressing rapidly. Different types of clocks, using different atoms and different kind of transitions allow extremely complete tests of fundamental physics: stability of fundamental constants, probing gravity and couplings to other interactions. Redondancy is important in case violations are seen. Space projects. Further improvements ? Higher frequencies (UV-X) ? Nuclear transitions ? Molecular transitions ?