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Searching for temporal variation of the fine-structure "constant"
in
radio-frequency transitions of Dy
Dmitry Budkerhttp://socrates.berkeley.edu/~budker
Dimensionless fundamental constant
Characterizes the strength of all electromagnetic interactions
FineFine--Structure Constant Structure Constant αα
2 1 [0.70 ppb]137.035 999 710 (96)
ec
α = =
Energy of atomic levels ∝ mec2·α2 ·(1+kα2+…)
G. Gabrielse et al, Phys. Rev. Lett. 97, 030802 (2006)
Professor Enrico Fermi
A gross variation
We search We search for for smallsmalltemporal temporal
variation of variation of aa
Are the constants of Nature constant?(A fundamental question)
Sir A. EddingtonA. EinsteinP. A. M. DiracE. TellerG. GamowR. H. Dicke…
2006 Templeton Foundation Award
The constants: Dimensionless combinations do not
depend on units :
Conventional Wisdom:
a,β,g-constant; δ~t-1,ε~t-1
Dirac’s Large Number Hypothesis and variations :
Ruled out as predict variations ~ 10-10-10-12/y
Dirac’s Large Number Hypothesis:
401 2 2
240
2
380
size of Universe 10classical electron radius /
Electromagnetic force between , 10Gravitational force between ,
Number of protons in Universe 10
e
e p
p
ctNe m c
e p eNe p Gm m
c tNGm
= = ≈
= = ≈
= ≈ ≈
1 2N N N t≈ ≈ ∝
Large variations are out…
… but BIG QUESTIONS are in:Are there small changes of “constants” over the past 13 Gy or so ?
May the “constants” be changing as we speak ?
Laboratory ?
Observations
Astrophysical searches for α-variation
or QSO
Astrophysical evidence for smaller α in the past:
J. K. Webb, et al. , Phys. Rev. Lett. 87, 091301 (2001)
α/α (× 10-16 /yr)
J. K. Webb, et al. , Phys. Rev. Lett. 87, 091301 (2001)7.2 ± 1.82001
2003
1999
M. T. Murphy, et al. , Mon. Not. R. Astron. Soc. 345, 609 (2003)6.4 ± 1.4
J. K. Webb, et al. , Phys. Rev. Lett. 82, 884 (1999)14 ± 5
Astrophysical evidence for a smaller α in the past:
Victor V. Flambaum
However, other groups see no variation:(using a different telescope and higher quality but smaller data set)
α/α (× 10-16 /yr)
R. Srianand, et al. , Phys. Rev. Lett. 92, 121302 (2004)0.6 ± 0.62004
2004 R. Quast, et al. , Astron. Astrophysics. 415, L7 (2004)0.5 ± 4
More Controversy: claim for variation of /p em mμ =
These measurements are based on the different dependences of molecular energies on μ:
• Electronic• Vibrational • Rotational
2em α∝
2 ee
p
mmm
α∝2 e
ep
mmm
α∝
More Controversy: limit on variation of /p em mμ =
arXiv.org > astro-ph > arXiv:0704.2301
Laboratory Searches
Looking for present-day variation [e.g., ]Level of present interest: 1/105 per 10 GyWhich is 1/1015 per year (assuming linear variation) This is about where best atomic clocksbest atomic clocks are todayClock laboratories search for variation of constants(We do not rely on fancy clock, but still would like to have one )
( )t nowα =
Laboratory limits (1σ):
Jason E. Stalnaker
Rapid progress with trapped single ions and femtosecond
frequency combs !
αα--Variation in Atomic DysprosiumVariation in Atomic Dysprosium
Two nearly degenerate states in dysprosium (Dy, Z=66) are highly sensitive to α-variation:
A B
Ground State0
20,000
Ener
gy (c
m-1
)
For α/α ~ 10-15 /yr
⇒ dΔ/dt ~ 2 Hz/yr !!
AB
Δ
Δ ~ (3-1000) MHz
dΔ/dt ~ 2×1015 Hz α/α
Dzuba, Flambaum, Kozlov, et al
Opposite parity
ΔE ~ 3-1000 MHz
⇒ E1 transition connecting the states can be driven with rf electric field
⇒ small enough to allow accurate direct counting of transition frequency
⇒ relaxed requirements on reference clock (∆υ/ υ)
A and B StatesA and B States
Statistical SensitivityStatistical Sensitivity
Transition linewidth ~ 20 kHz
Counting rate ~ 109 s-1
T1/2⇒ Sensitivity: δν ~ 0.6 Hz s1/2
After an hour of data taking, δν ~ 10 mHz which allows
for a sensitivity of
|α/α| ~ 5 x 10-18 /yr !!
833 nm
669 nm
1397 nm (b.r. ~ 30%)
E V E N O D D
J=10 A19797.96 cm-1
τ = 7.9 μs
B J=1019797.96 cm-1
τ > 200 μs
J=8 G
e J=8τ = 16 μs
J=9 f 26955.00 cm-1
τ = 0.5 μs
c J=9
PopulationPopulation
•Three-step scheme:
3rd - spontaneous emission
1st & 2nd - cw laser excitation
564 nm
E V E N O D D
J=10 A19797.96 cm-1
τ = 7.9 μs
B J=1019797.96 cm-1
τ > 200 μs
J=8 G
e J=8τ = 16 μs
J=9 f 26955.00 cm-1
τ = 0.5 μs
c J=9
rf Transition and Detectionrf Transition and Detection
• rf E-field excites atoms to state A
• State A decays and 564-nm light is detected
rf E-Field
The experiment evolved from a parity nonconservation parity nonconservation search in Dy
ApparatusApparatus
669-nm light
833 nm light
light pipe
interference filter
OVEN
PMT
mirror
Interaction Region
Interaction RegionInteraction Region
Experimental SetupExperimental Setup
50 Ω
PMT
Lock-InAmplifier
10 kΩ
Data Acquisitionand Control
RGA
CDMAClock
Cs AtomicClock
10 kHz ModulationFrequency
to E-Field Plates
rf Amplifier
FrequencyCounter
rf SynthesizerHigh-Vacuum
Chamber-6(~10 Torr)
Dr. A.-T. Nguyen, UCBöLANL
Arman CingÖz
3.04 3.06 3.08 3.1 3.12FrequencyHMHzL
0.5
1
1.5
2
kcoL-
nilangiSHV
smr
L
3.1-MHz Transition - 12ê16ê03 - File: 1216.025
First DataFirst Data
Amplitude Modulation:
ν0 = 3 073 937(52) Hz
rf Frequency Modulationrf Frequency Modulation
3.04 3.06 3.08 3.1 3.12rf Frequency HMHzL
-0.01
-0.005
0
0.005
0.01
0.015
0.02
1ts
cinomra
HHV
smr
L
041304.025 - 1st Harmonic
ν0 = 3 073 945(20) Hz
Fixed Frequency TechniqueFixed Frequency Technique
1st Harmonic 2nd Harmonic
Measure the normalized by the
Ratio (1st/2nd) = const.(ν - ν0)
A.- T. Nguyen et al. PRA Phys. Rev. A 69, 022105 (2004)
Systematic Effects
• However, it is not the size but the stability of these effects that is important
⇒ preliminary analysis shows that systematic effects can be controlled to
a level corresponding to |α/α| ~ 5 x 10-18 /yr.
Since Dy has many isotopes (some with hfs), more than one rf transition frequency can be measured
ω1
ω2
For example, two transition frequencies can be simultaneously measured:
Powerful Check for SystematicsPowerful Check for Systematics
ω1 + ω2 ⇒ insensitive to α variation
ω1 - ω2 ⇒ α variation is twice as large
Collisions with residual background atoms perturbs a radiating (absorbing) Dy atom
⇒ lineshape broadening and shift
Collisional effects in high-vacuum (10-6 Torr) have rarely been measured
Simple estimate:
σ ~ 10-14 cm2
n > 3x1010 molecules/cm3 at 1μTorr
v > 4x104 cm/s
⇒ δν ~ (2π)-1 n σ v = 2 Hz
Collisional EffectsCollisional Effects
Collisional DataCollisional Data
Collisional Shifts due to N2
y = 1.63 (4) x - 119 (2)
y = -1.61 (2) x + 115 (1)
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90 100
N2 Pressure (μTorr)
ν0 -
234
661
000
(Hz)
-100
-80
-60
-40
-20
0
20
40
60
80
100
ν0
- 3 0
74 0
00 (H
z)
235 MHz 3.1 MHz
Collisional ShiftsCollisional Shifts
235-MHz3.1-MHzGas
+2.75 (10)+2.78 (9)+2.14 (11)
< 5+1.72 (7)-0.02 (6)-1.27 (6)-0.09 (8)
-2.21 (7)Ar
-0.02 (4)H2
-2.74 (7)Xe-2.78 (7)Kr
-1.97 (30)O2
-1.71 (5)N2
-0.01 (3)Ne+1.25 (3)He
Shift Coefficients (Hz/μTorr)
Conclusion:⇒ collisional effects are consistent with those found
in 1-Torr measurements
Laser Detuning EffectLaser Detuning Effect
Laser Detuning Effect for 235-MHz Transition
Sign
al (a
rb. u
nits
)
0
50
100
150
200
-120 -100 -80 -60 -40 -20 0 20 40 60 80 100
833-nm Laser Freq. (MHz)ν
o - 2
34 6
61 0
00 (H
z)
Laser Detuning Effect for 754-MHz Transition
Sign
al (a
rb. u
nits
)
-1000
-600
-200
200
600
1000
-100 -80 -60 -40 -20 0 20 40 60 80
833-nm Laser Freq. (MHz)
νο -
753
513
000
(Hz)
Results
(-0.3 ± 3.6) x 10-15 yr-1 (-5.0 ± 3.7) x 10-15 yr-1
-0.6 ± 6.5 Hz/yr 9.0 ± 6.7 Hz/yr
α/α =.
α/α = (-2.9 ± 2.6mostly syst) x 10-15 yr-1. Independent of other
fundamental constants
Result: Phys. Rev. Lett. 98, 040801 (2007)
The Future