Testing the stability of
fundamental constants with
atomic clocks
Paris, France
❏ Bureau National de Métrologie – SYstèmes de Référence
Temps-Espace
H. 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)
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
1
Testing the stability of the fine structure
constant with atomic clocks - Motivations
❏ Theoretical predictions
– Unified theories allow a variation of
fundamental constants with time and space
T. Damour et al., Nucl. Phys. B 423, 532 (94)
– Recent prediction : the present drift rate of a
could 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) z = 2 ⇔ T ~ 10 Gyr
∆α
= − (0.72 ± 0.18 )× 10 −5 ; 0.5 < z < 3.5
α
Webb et al., Phys. Rev. Lett. 87, 091301 (01)
❏ Interesting range for new laboratory
experiments
α&
≤ 10 −15 yr −1
α
2
Testing the stability of the fine structure
constant with atomic clocks - Method
❏ Frequency of electronic transitions in atoms
and ions
ν i ≈ R y × f i (α )
– fi(a) includes relativistic effects, many-body
effects, spin-orbit coupling
• Dzuba et al., PRA 59, 230 (99)
æ ν ö æ α ∂f 2 α ∂f1 ö δα
÷÷ ×
δ lnçç 2 ÷÷ = çç
−
è ν 1 ø è f 2 ∂α f1 ∂α ø α
❏ Frequency of the ground hyperfine transition in
alkali-like atoms and ions
ν HFS
me 2
≈ Ry × g I
α × F (Z , α )
mp
❏ Atomic frequency comparisons
– Optical vs optical: (ν2/ ν1)~ f2(a)/ f1(a) Þ 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)
3
Sensitivity to a variations: coefficients
❏ Electronic transitions ν i ≈ R y × f i (α )
❏ Hyperfine transitions ν HFS ≈ Ry × g I
me 2
α × F (Z , α )
mp
❏ Mercury 199Hg+ and neutral 40Ca optical clocks
α ∂f Hg +
α ∂f Ca
≈ −3.2 ;
≈ +3.0 × 10 − 2
f Hg + ∂α
f Ca ∂α
–
–
199Hg+:
strong sensitivity to a; negative sign
87Sr should be calculated
❏ Rubidium 87Rb, cesium 133Cs and mercury
199Hg+ microwave clocks
α ∂FHg +
α ∂FCs
α ∂FRb
≈ +0.74;
≈ +2.2
≈ +0.30;
FRb ∂α
FCs ∂α
FHg + ∂α
❏ Sensitivity to a variations:
–
–
–
199Hg+(optical)
vs Cs(hfs): -6.0
87Rb(hfs) vs 133Cs(hfs) : -0.44
199Hg+(hfs) vs H : +2.2
4
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
5
The cryogenic spherical quadrupole trap
❏ Ring inner
diameter: 0.8 mm
❏ Radial secular
frequency:
νr ~1.2 MHz
❏ High collection
efficiency
❏ T=4 K
❏ Lifetime of a single
ion in the trap:
>3 months
6
Laser stabilization scheme at 563 nm
❏ Frequency fluctuations of the dye laser are
corrected with high bandwidth (~2 MHz)
❏ The reference cavity has high finesse
(F ~ 200000) and high stability
❏ The long term drift of the reference cavity (40
mHz.s-1 to several 100 mHz.s-1) is
compensated
7
Spectroscopy of the clock transition
❏ 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
~ 6.5 Hz
Tprobe = 120 ms
8
Systematic frequency shifts in the 199Hg+
optical clock
❏ Uncertainties (preliminary)
– Corrections and 1s uncertainties in Hz at
1.06×1015 Hz (282 nm)
Effect
Second order Zeeman effect
@ B=2.7 G
Black Body radiation shift
@ T=300K
Black Body radiation shift
@ T=4K
Second order Doppler
secular motion
Second order Doppler
micromotion
4
Background collisions ( He)
Quadrupole shift
-2
@ ∇E=10 V.mm
Correction Uncertainty
+1 386
3.4
+0.079
<0.01
0
0
<0.003
0.003
<0.1
0.1
0
0
<1
<1
Quadratic sum
NIST F1+ Maser ensemble
3.7
4
❏ Accuracy (preliminary)
– 10 Hz at 282 nm ⇔ 10-14
❏ Improvements Þ accuracy < 10-16
9
Phase-coherent RF to optical frequency
measurement - All optical clock
❏ For absolute optical frequency measurements
– Precision RF sources and frequency counter
are referenced to a primary standard (NIST
maser ensemble + NIST-F1)
❏ All optical clock
– fb and f0 are referenced to fr
– The clock output is fr=fHg+/m (m~106)
10
Measurements of the 199Hg+ clock frequency
❏ 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
νHg+ = 1 064 721 609 899 143.7 Hz
❏ Stability of νHg+/νCs :
d æ ν Hg + ö
÷÷ < 7 × 10−15 yr −1
lnçç
dt è ν Cs ø
Th. Udem et al. PRL 86, 4996 (2001)
S.A. Diddams et al. Science 293, 825 (2001)
11
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 to
define the SI unit of time
12
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
13
87Rb
cold atom fountain
14
Spectroscopy of the clock transition:
Ramsey fringes
1.0
1.0
0.8
0.6
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
0.2
0.0
-100
-50
0
50
100
detuning (Hz)
❏ 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
15
Systematic frequency shifts in atomic
fountains
❏ Fractional corrections and uncertainties (×1015)
Effect
Second order Zeeman
Black Body radiation shift
Cold collisions
Cavity pulling
Recoil
Residual First order Doppler
Background collisions
Ramsey and Rabi pulling
Microwave leakage
Correction Uncertainty
-177
0.5
+173
0.2
+9.5
0.5
0
0
0
0
0
Quadratic sum
0.1
0.4
0.1
0.1
0.1
0.9
❏ Typical accuracy of a fountain frequency standard:
1 part in 1015
❏ Typical systematic uncertainty in the Rb vs Cs
frequency comparison:
1.4 part in 1015
❏ Improvements Þ accuracy of a few parts in 1016
16
Fountain ensemble at BNM-SYRTE
17
Rb vs Cs frequency comparisons
-14
Maser Frequency (10 )
❏ 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 of
imperfect overlap
Pharao
15
FO1
Rb
10
5
2/27/00
3/28/00
4/27/00
❏ Results: νRb = 6 834 682 610.904 324 (10) Hz
d æ ν Rb ö
÷÷ = (0.2 ± 7.0) × 10−16 yr −1
lnçç
dt è ν Cs ø
18
Summary
❏
199Hg+(optical)
vs 133Cs(hfs) at NIST:
d æ ν Hg + ö
÷÷ < 7 ×10 −15 yr −1
lnçç
dt è ν Cs ø
me 6.0 ö÷
d æç
ln g Cs
α
< 7 × 10 −15 yr −1
÷
dt çè
mp
ø
ArXiv:physics/0212109
Accepted for publication in Phys. Rev. Lett.
❏
87Rb(hfs)
vs 133Cs(hfs) at BNM-SYRTE:
d æ ν Rb ö
÷÷ = (0.2 ± 7.0) ×10 −16 yr −1
lnçç
dt è ν Cs ø
d æ g Cs 0.44 ö
lnçç
α ÷÷ = (0.2 ± 7.0) × 10 −16 yr −1
dt è g Rb
ø
ArXiv:physics/0212112
Accepted for publication in Phys. Rev. Lett.
❏ Under the assumption that a alone is changing, these
results can be compared to previous work:
– Prestage et al., Phys. Rev. Lett 74, 3511 (95):
•
199Hg+(hfs)
vs H(hfs)
d
ln (α ) < 3.7 × 10 −14 yr −1
dt
– This work: improvement by a factor ~25-30
d
ln (α ) < 1.4 × 10 −15 yr −1
dt
19
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 be
possible
❏ 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 be
possible
❏ New tests with other clocks using the powerful
femtosecond laser based method for optical
frequency comparisons
– Neutral 40Ca at NIST
– Neutral 87Sr at BNM-SYRTE
20