Optical clocks, present and Optical clocks, present and future fundamental physics tests future fundamental physics tests

Optical clocks, present and Optical clocks, present and future fundamental physics tests future fundamental physics tests

Pierre Lemonde

LNE-SYRTE

Fractional accuracy of atomic clocksFractional accuracy of atomic clocksFractional accuracy of atomic clocksFractional accuracy of atomic clocks

Systematic effects-accuracySystematic effects-accuracySystematic effects-accuracySystematic effects-accuracy

• Zeeman effect: – Independent on the clock transition frequency

• Spectral purity, leakage,...: – Independent on the clock transition frequency

• Cold collisions: – Independent on the clock transition frequency

• Neighbouring transitions: – Independent on the clock transition frequency

• 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

@ Optical frequencies all these effects seem controllable at 10-18 or better !

Potential gain 104

Potential gain 104

Potential gain 104

Potential gain 104

Potential gain 102

Ultimate gain on the frequency stability : 104

Ultimate gain on the frequency accuracy > 102

Key ingredients

-A « good » clock transition

-Ability to control external degrees of freedom.

-Ultra-stable lasers

Interest of optical clocksInterest of optical clocksInterest of optical clocksInterest of optical clocks

<10-18

Q~4 1014, N~106, Tc ~ 1s

Single ion clocks an neutral atom lattice clocks are two possible ways forward

Multipolar couplings: E2, E3

Intercombination transitions

Quantum references: ions or atomsQuantum references: ions or atomsQuantum references: ions or atomsQuantum references: ions or atoms

2P1/2

Sr+ (NPL,NRC)

=0.4Hz2S1/2

2P1/2

2D5/2

422 nm674 nm

2S1/2

2D3/2

2F7/2

Yb+(PTB, NPL)

369 nm 436 nm

467 nm

=3 Hz

=10-9 Hz

Other ions: Hg+ (NIST), Ca+(Innsbruck, Osaka, PIIM)

Sr (Tokyo, JILA, SYRTE,…), Yb (NIST, INRIM, Tokyo,…) Hg (SYRTE, Tokyo), In+

=1 mHz1S0

1P1

3P0

461 nm698 nm

=8 mHz1S0

1P1

3P0

167 nm267 nm

Al+ (NIST)

Quantum logic clockQuantum logic clockQuantum logic clockQuantum logic clock

One logic ion for cooling and detection

One clock ion for spectroscopy

External degrees of freedom are coupled via Coulomb interaction

Al+ clocksAl+ clocksAl+ clocksAl+ clocks

C. Chou et al. PRL 104 070802 (2010)

C. Chou et al. Science 329, 1630 (2010)

Al+ clock accuracy budgetAl+ clock accuracy budgetAl+ clock accuracy budgetAl+ clock accuracy budget

C. Chou et al. PRL 104 070802 (2010)

Ion clock with sub 10-17 accuracy

Neutral atom clocksNeutral atom clocksNeutral atom clocksNeutral atom clocks

Trapping neutral atomsTrapping neutral atomsTrapping neutral atomsTrapping neutral atoms

Trapping : dipole force(intense laser)

-0.5

-0.25

0

0.25

0.5

0

0.5

1

-10

-7.5

-5

-2.5

0

-0.5

-0.25

0

0.25

0.5

0

0.5

1

/2

Confinement : standing wave

Optical lattice clocks

Trap shifts

> 10-10

reaching 10-18, effect must be controlled to within 10-8

Problems linked to trappingProblems linked to trappingProblems linked to trappingProblems linked to trappingTrap 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 problemSolution to the trapping problemSolution to the trapping problemSolution 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

1S0

3D1

3S1

1P1

3P0

698 nm

461 nm2.56 µm

679 nmSr

M. Takamoto et al, Nature 453, 231 (2005)

1S0

3P0

m : "longueur d'onde magique"

Experimental setupExperimental setupExperimental setupExperimental setup

Ultra-narrow resonanceUltra-narrow resonance

Lattice clock comparisonLattice clock comparison

Trap effectsTrap effects

E2-M1 Effects E2-M1 Effects E2-M1 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

E2-M1 Effects E2-M1 Effects E2-M1 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

This leads to a clock shift

E2-M1 effectsE2-M1 effects E2-M1 effectsE2-M1 effectsMeasurements

The shift is measured by changing n and the trap depth U0=100-500 Er

•The effect is not resolved, not a problem

•Upper bound 10-17 for U0=800 Er

Trap shiftsTrap shifts

•Hyperpolarisability

<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

8787Sr lattice clock accuracy budgetSr lattice clock accuracy budget8787Sr lattice clock accuracy budgetSr 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 ?

Towards a Hg lattice clockTowards a Hg lattice clockTowards a Hg lattice clockTowards 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 worldwideOptical 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 comparisonsClock comparisons

• « Round-trip » method for noise compensation

Round-trip noise detection

LAB 1

AccumulatedPhase noise

Ultra-stable 1.542 µm laser

Noise correction

LAB 2P

P

Link instabilitymeasurement

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 groundFundamental tests on ground

• Stability of fundamental constants expected improvement by 2 orders of magnitude 10-18/yr limited by microwave clocks. Possible improvements if

nuclear transitions are used.

• Dependence of to local gravitational potential– Expected improvement by 2 orders of magnitude 10-8 (GM/rc2)

• Massive redondancy due to the large number of atomic species/transitions

Optical clocks in spaceOptical 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 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

main requirements:1. compact design2. reliability3. low power consumption

optical breadboard 120 cm x 90 cm

Transportable Strontium Source (LENS/U.Firenze)-SOC projectTransportable Strontium Source (LENS/U.Firenze)-SOC project

main planning choices:1. compact breadboard for frequency production2. all lights fiber delivered3. custom flange holding MOT coils and oven with 2D cooling

Schioppo et al, Proc. EFTF (2010)

ConclusionsConclusionsConclusionsConclusions

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 ?