Des horloges atomiques Des horloges atomiques pour LISA ?pour LISA ?

Des horloges atomiques Des horloges atomiques pour LISA ?pour LISA ?

Pierre LemondeBureau National de Métrologie – SYRTE (UMR CNRS 8630)

Observatoire de Paris, France

Journées LISA-FRANCEAnnecy, Janvier 2007

LISA frequency noise cancellationLISA frequency noise cancellationLISA frequency noise cancellationLISA frequency noise cancellation

S(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 sFlicker 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

Stability of a laser stabilized to atomic Stability of a laser stabilized to atomic resonancesresonances

Stability of a laser stabilized to atomic Stability of a laser stabilized to atomic resonancesresonances

0

1

atomic resonancemacroscopic 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.

Detection

Nat ~2109

r ~mm

T ~1K

ΔV ~2 cm.s-1

Vlaunch ~ 4m.s-1

H ~1m

T ~500ms

Tc ~0.8-2s

Selection

3

2

1

Atomic fountains: Principle of operationAtomic fountains: Principle of operationAtomic fountains: Principle of operationAtomic fountains: Principle of operation

-100 -50 0 50 1000.0

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-1.0 -0.5 0.0 0.5 1.00.0

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1.0

detuning (Hz)

0.94 Hz

tran

sitio

n pr

obab

ility

P

NO AVERAGING

ONE POINT = ONE MEASUREMENT OF P

Ramsey fringes in atomic fountainRamsey fringes in atomic fountainRamsey fringes in atomic fountainRamsey fringes in atomic fountain

Fluctuations of the transition probability:

We alternate measurements on bothe sides of the central fringe to generate an error signal, whichis used to servo-control the microwave source

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

(~ 310-15 @ 1s)

Frequency stability with a cryogenic Oscillator Frequency stability with a cryogenic Oscillator Frequency stability with a cryogenic Oscillator Frequency stability with a cryogenic Oscillator

Fountain AccuracyFountain AccuracyFountain AccuracyFountain Accuracy

Fountain (LNE-SYRTE) FO2(Cs)

second order Zeeman 1920.4 (0.1)

Blackbody radiation -168.7 (0.6)

Collisions + cavity pulling -129.3 (1.3)

Residual Doppler effect 0.0 (3.0)

Recoil 0.0 (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)

Total 3.8

Effect Shift and uncertainty (10-16)

Going further: Two possible waysGoing further: Two possible waysGoing further: Two possible waysGoing further: Two possible ways

0

1

atomic resonancemacroscopic 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

Optical frequency standards ?Optical frequency standards ?Optical frequency standards ?Optical frequency standards ?

Frequency stability :

Increase (x 105)

Frequency accuracy: most of the shifts (expressed in absolute values) don't dependon 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 togetherwith an accuracy around 10-14.

Doppler EffectDoppler EffectDoppler EffectDoppler Effect

Atomic fountains limited to ~ 10-16

Calcium optical clock ~ 10-15

vRoom 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> = 0Residual Doppler shift ~ 10-16

Can the Doppler frequency shift be decreased down to ~ 10-18 ????

Doppler shift is given by k.v, independant on 0 in fractional units

Doppler/recoil, quantum pictureDoppler/recoil, quantum pictureDoppler/recoil, quantum pictureDoppler/recoil, quantum picture

2-level atom:

coupling: acts on internal and external degrees of freedom

Free atoms : eigenstates of Hext have a well defined momentum (plane waves)

p

E

Ef

Ee

resonance

frequency shift

Doppler recoil

is the translation operator by hks in momentum space

Doppler/recoil, trapped particlesDoppler/recoil, trapped particlesDoppler/recoil, trapped particlesDoppler/recoil, trapped particles

2-level atom:

coupling:

Trapped atoms : eigenstates of Hext are more and more localized (delocalized) in real (momentum) spaceas t increases.

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

Tight confinement of atomsTight confinement of atomsTight confinement of atomsTight confinement of atoms

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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 (E2) and polarization are difficult to control at a « metrological » level.Relevant parameter is the difference between both clock levels shit.

/2

atoms

An optical clock with trapped atomsAn optical clock with trapped atomsAn optical clock with trapped atomsAn optical clock with trapped atoms

Katori, Proc. 6th Symp. Freq. Standards and Metrology (2002)Pal’chikov, Domnin and Novoselov J. Opt. B. 5 (2003) S131Katori et al. PRL 91, 173005 (2003)

Clock transition 1S0-3P0 transition (=1mHz)

Atoms confined in an optical lattice. Light shift cancellation at the magic wavelengthof the lattice. Similar scheme with Yb, Hg, Mg, Ca…

1S0

3D1

3S1

1P1

3P0

698 nmTransition horloge

(~1 mHz)

461 nm2.56 µm

679 nm

87Sr3P0813 nm

2,56 µm

679 nm

Dep

lace

men

t lu

min

eux

Longeur d'onde

461 nm

1S0

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 setupExperimental setupExperimental setupExperimental setup

Longitudinal temperature given by sidebands ratio

Tz = 2 µK, 95 % of the atoms in |nz=0>

1S0

nz=0

3

2

1

Groundstate

Excitedstate

3P0

nz=0

3

2

1

Longitudinal sidebands frequency depends on the transverse excitation. Shape of sidebands gives the transverse temperature. Tr = 10 µK

Optical lattice clocks: state of the artOptical lattice clocks: state of the artOptical lattice clocks: state of the artOptical lattice clocks: state of the art

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0.0

0.1

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Tra

nsi

tion

pro

ba

bili

ty

detuning [kHz]

A. Brusch et al. PRL 96, 103003 (2006)

Optical lattice clocks: state of the artOptical lattice clocks: state of the artOptical lattice clocks: state of the artOptical 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.

Optical lattice clocks: state of the artOptical lattice clocks: state of the artOptical lattice clocks: state of the artOptical 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…

40

80

120

160

f Sr -

42

9 2

28

00

4 2

29

80

0 H

z

Ludlow et al. RPL 93 033003 (2006)

Takamoto et al. Nature 435, 321 (2005)

J. Ye et al. Proc. ICAP 2006

Le Targat et al. PRL 97 1308001 (2006)

Takamoto et al. arXiv:physics/0608212

Differential light shift cancellation ?Differential light shift cancellation ?Differential light shift cancellation ?Differential light shift cancellation ?

Feasibility is conditioned by the magnitude of higher order effects

=> Scale as E4 U02 Higher order terms : Hyperpolarisability

Neutral atoms in an optical lattice :

At the magic wavelength, the first order term cancels

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

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

Optical lattice clocks: milestonesOptical lattice clocks: milestonesOptical lattice clocks: milestonesOptical 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

Towards space optical clocksTowards space optical clocksTowards space optical clocksTowards space optical clocks

Main technologies are common to the PHARAO project

optical clocks in space : ESA project (cosmic vision)