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

2. Fractional accuracy of atomic clocks

3. 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: , Sr, Yb ~ , Hg : , Al
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 or better !

4. 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

5. 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)

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

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

8. Al+ clock accuracy budget
Ion clock with sub accuracy
C. Chou et al. PRL (2010)

9. Neutral atom clocks

10. 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

11. 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 : at least 10 Er (i.e. 36 kHz, or in fractional units for Sr)
Both states are shifted. The differential shift should be considered
P. Lemonde, P. Wolf, Phys. Rev. A (2005)

12. 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)

13. Experimental setup

14. Ultra-narrow resonance

15. Lattice clock comparison

16. Trap effects

17. 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

18. 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

19. 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= 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 for U0=800 Er

20. 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

21. 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 ?

22. 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 (21) nm
L. Yi et al., Phys. Rev. Lett. 106, (2011)

23. 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

24. 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 level over hundreds of km over telecom network
Global comparisons = satellite based systems
ACES-MWL down to a few 10-17, L. Cacciapuoti (next talk)
Mini-DOLL coherent optical link, K. Djerroud et al. Opt. Lett. 35, 1479 (2009)

25. 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

26. 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

27. 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

28. Conclusions
Optival clocks with ions and neutrals now clearly outperform microwave standards. Present accuracy and long term stability
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 ?