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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
LISA frequency noise cancellation
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.
Sn(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 s
Flicker floor about 4 10-15
Doing better: cold atoms
Stability of a laser stabilized to atomic
resonances
atomic resonance
macroscopic oscillator
1
correction
atoms
interrogation
0
Short term frequency stability:
atomic quality factor
Long term frequency stability: control of systematic effects. 10-15@1s=> 3 10-18@1000 s.
+ transition should be insensitive to
external perturbations
Atomic fountains: Principle of operation
Nat ~2109
r ~1.5-3mm
T ~1mK
ΔV ~2 cm.s-1
Selection
3
2
4m.s-1
Vlaunch ~
H ~1m
T ~500ms
Tc ~0.8-2s
1
Detection
Ramsey fringes in atomic fountain
1.0
1.0
0.8
0.6
transition probability P
0.4
0.8
0.94 Hz
0.2
0.0
-1.0 -0.5 0.0
0.5
1.0
0.6
0.4
NO AVERAGING
ONE POINT = ONE
MEASUREMENT OF P
0.2
0.0
-100
-50
0
50
100
detuning (Hz)
We alternate measurements on bothe sides of the central fringe to generate an error signal, which
is used to servo-control the microwave source
Fluctuations of the transition probability:
Frequency stability with a cryogenic Oscillator
With a cryogenic sapphire
oscillator, low noise microwave
synthesis
(~ 310-15 @ 1s)
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!
Fountain Accuracy
Fountain (LNE-SYRTE)
Effect
FO2(Cs)
Shift and uncertainty (10-16)
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
Going further: Two possible ways
atomic resonance
macroscopic oscillator
1
correction
atoms
interrogation
0
atomic quality factor
-as high as possible
-low natural width
-Fourier limit, long interaction time
-low oscillator spectral width
-Large atom number
-low noise detection scheme
-low noise oscillator
+ transition should be insensitive to
external perturbations
Atomic transition in the optical domain
A clock in space
Optical frequency standards ?
Frequency stability :
Increase
(x 105)
Optical fountain at the quantum limit
!!!!!!!!!
Frequency accuracy: most of the shifts (expressed in absolute values) don't depend
on the frequency of the transition (Collisions, Zeeman...).
-Ability to compare frequencies (no fast enough electronics )
Three major difficulties
-Recoil and first order Doppler effect
-Interrogation oscillator noise conversion (Dick effect).
The best optical clocks so far exhibit frequency stabilities in the 10-15 t -1/2 range together
with an accuracy around 10-14.
Doppler Effect
Doppler shift is given by k.v, independant on n0 in fractional units
v
Room 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> = 0
Residual Doppler shift ~ 10-16
Atomic fountains limited to ~ 10-16
Calcium optical clock ~ 10-15
Can the Doppler frequency shift be decreased down to ~ 10-18 ????
Doppler/recoil, quantum picture
2-level atom:
Free atoms :
eigenstates of Hext have a well defined
momentum (plane waves)
acts on internal and external
degrees of freedom
coupling:
is the translation operator by hks in momentum space
E
resonance
Ee
frequency shift
Ef
p
Doppler
recoil
Doppler/recoil, trapped particles
2-level atom:
eigenstates of Hext are more and more
localized (delocalized) in real (momentum) space
as wt increases.
Trapped atoms :
coupling:
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 atoms
1
0.5
Laser 1
atoms
0
Laser 2
0
-2.5
-5
-7.5
-10
-0.5
-0.25
0
0.25
l/2
0.5
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.
An optical clock with trapped atoms
3S
1
461 nm
679 nm
1P
1
3D
1
461 nm
1S
0
3P
0
2.56 µm
698 nm
Transition horloge
(~1 mHz)
Deplacement lumineux
87Sr
679 nm
3
813 nm
1
P0
S0
2,56 µm
Longeur d'onde
Katori, Proc. 6th Symp. Freq. Standards and Metrology (2002)
Atoms confined in an optical lattice.
Pal’chikov, Domnin and Novoselov J. Opt. B. 5 (2003) S131
Light shift cancellation at the magic wavelength
Katori et al. PRL 91, 173005 (2003)
of the lattice. Similar scheme with Yb, Hg, Mg, Ca…
Clock transition 1S0-3P0 transition (G =1mHz)
Experimental setup
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)
Optical lattice clocks: state of the art
0.4
Transition probability
3P
0.3
0
Excited
state
3
2
1
nz=0
0.2
1S
0
0.1
3
2
1
nz=0
0.0
-200
-100
0
100
200
detuning [kHz]
Longitudinal temperature given by sidebands ratio
Tz = 2 µK, 95 % of the atoms in |nz=0>
Longitudinal sidebands frequency depends on
the transverse excitation. Shape of sidebands
gives the transverse temperature. Tr = 10 µK
A. Brusch et al. PRL 96, 103003 (2006)
Ground
state
Optical lattice clocks: state of the art
Experimental resonance in a Sr optical lattice clock (JILA, Boulder).
Line-Q is four orders of magnitude larger than in an atomic fountain,
highest line-Q ever obtained for any form of coherent spectroscopy.
M. Boyd et al. Science 314, 1430 (2006)
Optical lattice clocks: state of the art
fSr - 429 228 004 229 800 Hz
160
Takamoto et al.
Nature 435, 321 (2005)
120
Ludlow et al.
RPL 93 033003 (2006)
Takamoto et al.
arXiv:physics/0608212
80
Le Targat et al.
PRL 97 1308001 (2006)
J. Ye et al.
Proc. ICAP 2006
40
-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…
Differential light shift cancellation ?
 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
 Neutral atoms in an optical lattice :
 At the magic wavelength, the first order term cancels
 Higher order terms : Hyperpolarisability
=> Scale as E4 a U02
 Feasibility is conditioned by the magnitude of higher order effects
 Experimentally demonstrated to be negligible for 10-18 accuracy (SYRTE,Sr)
 Actual control of the trap shift at a level of 10-7
A. Brusch et al. PRL 96, 103003 (2006)
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
Towards space optical clocks
 Main technologies are common to the PHARAO project
 optical clocks in space : ESA project (cosmic vision)