1

Testing the stability offundamental constants with

atomic clocks

Boulder, Colorado, USA❏ National Institute of Standards and Technology

S. Bize, S.A. Diddams, U. Tanaka, C.E. Tanner, W.H.Oskay, R.E. Drullinger, T.E. Parker, T.P. Heavner, S.R.Jefferts, L. Hollberg, W.M. Itano and J.C. Bergquist

Paris, France❏ Bureau National de Métrologie – SYstèmes de Référence

Temps-EspaceH. Marion, F. Pereira Dos Santos, M. Abgrall, S. Zhang, Y.Sortais, S. Bize, I. Maksimovic, D. Calonico, J. Grünert, C.Mandache, P. Lemonde, G. Santarelli, Ph. Laurent, A.Clairon and C. Salomon (LKB)

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Testing the stability of the fine structureconstant with atomic clocks - Motivations

❏ Theoretical predictions– Unified theories allow a variation of

fundamental constants with time and spaceT. Damour et al., Nucl. Phys. B 423, 532 (94)

– Recent prediction : the present drift rate of acould be as high as 10-16 yr-1

T. Damour et al., Phys. Rev. Lett 89, 081601 (02)

❏ Recent experiments– based on the observation of the spectrum of

quasars– measure a change of a on cosmological time

scale (at the 4σ level)

Webb et al., Phys. Rev. Lett. 87, 091301 (01)

❏ Interesting range for new laboratoryexperiments

GyrTz 10~2⇔=

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3

Testing the stability of the fine structureconstant with atomic clocks - Method

❏ Frequency of electronic transitions in atomsand ions

– fi(a) includes relativistic effects, many-bodyeffects, spin-orbit coupling

• Dzuba et al., PRA 59, 230 (99)

❏ Frequency of the ground hyperfine transition inalkali-like atoms and ions

❏ Atomic frequency comparisons– Optical vs optical: (ν2/ ν1)~ f2(a)/ f1(a) � a– Hyperfine vs optical:

(ν2/ ν1)~ g2(me/mp)a2 F(Z2, a)/f1(a)– Hyperfine vs hyperfine

(ν2/ ν1)~ g2F(Z2, a)/ g1F(Z1, a)

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ff

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4

Sensitivity to a variations: coefficients

❏ Electronic transitions

❏ Hyperfine transitions

❏ Mercury 199Hg+ and neutral 40Ca optical clocks

– 199Hg+: strong sensitivity to a; negative sign– 87Sr should be calculated

❏ Rubidium 87Rb, cesium 133Cs and mercury199Hg+ microwave clocks

❏ Sensitivity to a variations:– 199Hg+(optical) vs Cs(hfs): -6.0– 87Rb(hfs) vs 133Cs(hfs) : -0.44– 199Hg+(hfs) vs H : +2.2

2100.3;2.3 −+

+

×+≈∂∂−≈

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αα Ca

Ca

Hg

Hg

ff

ff

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2.2F

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FHg

Hg

Cs

Cs

Rb

Rb+≈

α∂∂α+≈

α∂∂α+≈

α∂∂α +

+

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Experiment at NIST: 199Hg+(optical) vs Cs(hfs)

❏ 199Hg+ ion: energy levels:

❏ Clock transition:– 282 nm ⇔ 1.06×1015 Hz– Electric quadrupole transition– Natural linewidth: ~ 2 Hz– Qat ~ 5×1014

❏ Laser cooling and detection:– 194 nm– Lifetime excited state: ~2 ns– Doppler cooling limit: 1.7 mK

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The cryogenic spherical quadrupole trap

❏ Ring innerdiameter: 0.8 mm

❏ Radial secularfrequency: νr ~1.2 MHz

❏ High collectionefficiency

❏ T=4 K❏ Lifetime of a single

ion in the trap:>3 months

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Laser stabilization scheme at 563 nm

❏ Frequency fluctuations of the dye laser arecorrected with high bandwidth (~2 MHz)

❏ The reference cavity has high finesse(F ~ 200000) and high stability

❏ The long term drift of the reference cavity (40mHz.s-1 to several 100 mHz.s-1) iscompensated

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❏ Beatnote between 2 stable light sources

– σy(τ)=3×10-16 for τ=1 to 30 s– below the quantum projection noise limited stability

of the 199Hg+ clock❏ Spectroscopy of the recoiless clock transition

– Atomic quality factor exceeding 1014

Spectroscopy of the clock transition

Tprobe = 120 ms

~ 6.5 Hz

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Systematic frequency shifts in the 199Hg+

optical clock

❏ Uncertainties (preliminary)– Corrections and 1s uncertainties in Hz at

1.06×1015 Hz (282 nm)

❏ Accuracy (preliminary)– 10 Hz at 282 nm ⇔ 10-14

❏ Improvements � accuracy < 10-16

Effect Correction UncertaintySecond order Zeeman effect @ B=2.7 G

+1 386 3.4

Black Body radiation shift @ T=300K

+0.079 <0.01

Black Body radiation shift @ T=4K

0 0

Second order Doppler secular motion

<0.003 0.003

Second order Doppler micromotion

<0.1 0.1

Background collisions (4He) 0 <1 Quadrupole shift @ ∇ E=10 V.mm-2

0 <1

Quadratic sum 3.7 NIST F1+ Maser ensemble 4

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Phase-coherent RF to optical frequencymeasurement - All optical clock

❏ For absolute optical frequency measurements– Precision RF sources and frequency counter

are referenced to a primary standard (NISTmaser ensemble + NIST-F1)

❏ All optical clock– fb and f0 are referenced to fr– The clock output is fr=fHg+/m (m~106)

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❏ Stability of the maser: σy(τ =1s)=2×10-13

❏ Contribution of the comb: σy(τ =1s)~2×10-14

❏ Stability of the Hg+ clock: σy(τ)=7×10-15 τ -1/2

❏ Stability of νHg+/νCs :

Th. Udem et al. PRL 86, 4996 (2001)S.A. Diddams et al. Science 293, 825 (2001)

Measurements of the 199Hg+ clock frequency

νHg+ = 1 064 721 609 899 143.7 Hz

115

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Hg yr107lndtd −−+ ×<��

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Experiment at BNM-SYRTE:87Rb(hfs) vs 133Cs(hfs)

❏ 87Rb atom: energy levels

❏ 133Cs energy levels:– Similar– The frequency of the hyperfine splitting of 133Cs

is conventionally set to 9 192 631 770 Hz todefine the SI unit of time

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Principle of operation of a cold atom fountain

❏ Nat~2×109

❏ σr~1.5−3mm❏ T~1µK

❏ V~4m.s-1

❏ H~1m❏ T~500ms

❏ Tc~0.8-2s

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87Rb cold atom fountain

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Spectroscopy of the clock transition:Ramsey fringes

❏ Teff=534 ms❏ Linewidth : 0.94 Hz❏ Atomic quality factor : Qat=9.82×109

❏ No averaging, one measurement of P per point❏ Noise on the measurement of P: σδP=3.3 ×10-4

❏ Signal to noise ratio : 1/σδP=3000

-100 -50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.5 0.0 0.5 1.00.0

0.2

0.4

0.6

0.8

1.0

detuning (Hz)

0.94 Hz

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Systematic frequency shifts in atomicfountains

❏ Fractional corrections and uncertainties (×1015)

❏ Typical accuracy of a fountain frequency standard:1 part in 1015

❏ Typical systematic uncertainty in the Rb vs Csfrequency comparison:

1.4 part in 1015

❏ Improvements � accuracy of a few parts in 1016

Effect Correction UncertaintySecond order Zeeman -177 0.5Black Body radiation shift +173 0.2Cold collisionsCavity pulling

+9.5 0.5

Recoil 0 0.1Residual First order Doppler 0 0.4Background collisions 0 0.1Ramsey and Rabi pulling 0 0.1Microwave leakage 0 0.1

Quadratic sum 0.9

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Fountain ensemble at BNM-SYRTE

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Rb vs Cs frequency comparisons

❏ Results: νRb = 6 834 682 610.904 324 (10) Hz

116

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Rb yr10)0.72.0(lndtd −−×±=��

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❏ Stability of a fountain vs the H-maser: σy(τ)~1.2×10-13 τ -1/2

❏ Frequency resolution between two fountains:σy(τ =1day)~1.1×10-15

❏ Additional contributions from H-maser in case ofimperfect overlap

2/27/00 3/28/00 4/27/00

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Summary

❏ 199Hg+(optical) vs 133Cs(hfs) at NIST:

ArXiv:physics/0212109Accepted for publication in Phys. Rev. Lett.

❏ 87Rb(hfs) vs 133Cs(hfs) at BNM-SYRTE:

ArXiv:physics/0212112

Accepted for publication in Phys. Rev. Lett.

❏ Under the assumption that a alone is changing, theseresults can be compared to previous work:– Prestage et al., Phys. Rev. Lett 74, 3511 (95):

• 199Hg+(hfs) vs H(hfs)

– This work: improvement by a factor ~25-30

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Prospects

❏ Improvements of the 199Hg+ clock– the magnetic field will be reduced– the electric-quadrupole shift will be measured– A second 199Hg+ clock has been constructed to

perform measurements with σy(τ)<10-14 τ -1/2

– Accuracy below 1 part in 1016 should bepossible

❏ Improvements of cold atom fountains– Improved method to continously measure the

cold collision shift– Use of SCO as interrogation oscillator to

perform measurements with σy(τ) ~ 10-14 τ -1/2

– Accuracy of a few parts in 1016 should bepossible

❏ New tests with other clocks using the powerfulfemtosecond laser based method for opticalfrequency comparisons– Neutral 40Ca at NIST– Neutral 87Sr at BNM-SYRTE