Searching for temporal variation of the fine

Searching for temporal variation
of the fine-structure "constant"
in
radio-frequency transitions of Dy
Dmitry Budker
http://socrates.berkeley.edu/~budker
Fine-Structure Constant α
z
z
Dimensionless fundamental constant
Characterizes the strength of all electromagnetic
interactions
z
Energy of atomic levels ∝ mec2·α2 ·(1+kα2+…)
e2
1
α=
=
[0.70 ppb]
=c 137.035 999 710 (96)
G. Gabrielse et al, Phys. Rev. Lett. 97, 030802 (2006)
A gross variation
We search
for small
temporal
variation of
a
Professor Enrico Fermi
Are the constants of Nature constant?
(A fundamental question)

Sir A. Eddington
A. Einstein
P. A. M. Dirac
E. Teller
G. Gamow
R. 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
-12
10 -10 /y
size of Universe
ct
40
= 2
≈
N1 =
10
classical electron radius e / me c 2
Electromagnetic force between e, p
e2
=
≈ 1040
N2 =
Gravitational force between e, p
Gme m p
c 3t
≈ 1080
N = Number of protons in Universe ≈
Gm p
Dirac’s Large Number Hypothesis:
N1 ≈ N 2 ≈ N ∝ t
Large variations are out…
… but BIG QUESTIONS are in:
Are there small changes of “constants” over the
past 13 Gy or so ?
Observations
May the “constants” be changing as we speak ?
Laboratory ?
Astrophysical searches for α-variation
or QSO
z
Astrophysical evidence for smaller α in the past:
J. K. Webb, et al. , Phys. Rev. Lett. 87, 091301 (2001)
z
Astrophysical evidence for a smaller α in the past:
α/α (× 10-16 /yr)
z
1999
14 ± 5
J. K. Webb, et al. , Phys. Rev. Lett. 82, 884 (1999)
2001
7.2 ± 1.8
J. K. Webb, et al. , Phys. Rev. Lett. 87, 091301 (2001)
2003
6.4 ± 1.4
M. T. Murphy, et al. , Mon. Not. R. Astron. Soc. 345, 609
(2003)
Victor V. Flambaum
z
However, other groups see no variation:
(using a different telescope and higher quality but smaller data set)
α/α (× 10-16 /yr)
z
2004
0.5 ± 4
R. Quast, et al. , Astron. Astrophysics. 415, L7 (2004)
2004
0.6 ± 0.6
R. Srianand, et al. , Phys. Rev. Lett. 92, 121302 (2004)
More Controversy: claim for variation of μ = m p / me
These measurements are based on the different dependences
of molecular energies on μ:
• Electronic ∝ meα 2
me
2
∝ meα
• Vibrational
m p ∝ m α 2 me
• Rotational
e
mp
More Controversy: limit on variation of μ = m p / me
arXiv.org > astro-ph > arXiv:0704.2301
Laboratory Searches

Looking for present-day variation [e.g., α (t = now)]
Level of present interest: 1/105 per 10 Gy
Which is 1/1015 per year (assuming linear variation)
This is about where best atomic clocks are today
Clock laboratories search for variation of constants
(We do not rely on fancy clock, but still would like to have one )
z
Laboratory limits (1σ):
Rapid progress with trapped
single ions and femtosecond
frequency combs !
Jason E. Stalnaker
α-Variation in Atomic Dysprosium
z
A
B
Energy (cm-1)
20,000
Two nearly degenerate states in dysprosium (Dy, Z=66)
are highly sensitive to α-variation:
B
A
Δ
Δ ~ (3-1000) MHz
dΔ/dt ~ 2×1015 Hz α/α
z
0
Ground State
For α/α ~ 10-15 /yr
z
⇒ dΔ/dt ~ 2 Hz/yr !!
Dzuba, Flambaum, Kozlov, et al
A and B States
z
Opposite parity
z
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)
Statistical Sensitivity
z
Transition linewidth ~ 20 kHz
z
Counting rate ~ 109 s-1
⇒ Sensitivity: δν ~ 0.6 Hz s1/2
T1/2
After an hour of data taking, δν ~ 10 mHz which allows
for a sensitivity of
|α/α| ~ 5 x 10-18 /yr !!
z
Population
•Three-step scheme:
1st & 2nd - cw laser
excitation
J=9
26955.00 cm-1
τ = 0.5 μs
J=10
19797.96 cm-1
τ = 7.9 μs
f
1397 nm
(b.r. ~ 30%)
A
669 nm
833 nm
3rd - spontaneous
emission
J=8
G
EVEN
ODD
B
J=10
19797.96 cm-1
τ > 200 μs
c
J=9
e
J=8
τ = 16 μs
rf Transition and Detection
J=9
26955.00 cm-1
τ = 0.5 μs
• rf E-field excites atoms
to state A
f
rf E-Field
J=10
19797.96 cm-1
τ = 7.9 μs
A
564 nm
• State A decays and
564-nm light is detected
J=8
G
EVEN
ODD
B
J=10
19797.96 cm-1
τ > 200 μs
c
J=9
e
J=8
τ = 16 μs
The experiment evolved from a
parity nonconservation search in Dy
Apparatus
t
h
g
li
m
n
3
3
8
OV
EN
Interaction Region
mirror
t
il gh
nm
9
66
light pipe
T
M
P
interference filter
Interaction Region
Experimental Setup
CDMA
Clock
Frequency
Counter
RGA
Cs Atomic
Clock
Data Acquisition
and Control
rf Synthesizer
rf Amplifier
to E-Field
Plates
High-Vacuum
Chamber
-6
(~10 Torr)
50 Ω
10 kHz Modulation
Frequency
PMT
Lock-In
Amplifier
10 kΩ
Dr. A.-T. Nguyen, UCBöLANL
Arman CingÖz
First Data
Amplitude Modulation:
3.1-MHz Transition - 12ê16ê03 - File: 1216.025
Lock-in Signal HV rmsL
2
ν0 = 3 073 937(52) Hz
1.5
1
0.5
3.04
3.06
3.08
FrequencyHMHzL
3.1
3.12
rf Frequency Modulation
041304.025
0.02
-
1st Harmonic
1st HarmonicHV rmsL
0.015
0.01
ν0 = 3 073 945(20) Hz
0.005
0
-0.005
-0.01
3.04
3.06
3.08
rf Frequency HMHzL
3.1
3.12
Fixed Frequency Technique
2nd Harmonic
1st Harmonic
Measure the
normalized by the
Ratio (1st/2nd) = const.(ν - ν0)
Systematic Effects
A.- T. Nguyen et al. PRA Phys. Rev. A 69, 022105
(2004)
• 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
Powerful Check for Systematics
Since Dy has many isotopes (some with hfs), more than
one rf transition frequency can be measured
For example, two transition frequencies can be simultaneously measured:
ω1
ω2
ω1 + ω2 ⇒ insensitive to α variation
ω1 - ω2 ⇒ α variation is twice as large
Collisional Effects
Collisions with residual background atoms perturbs a
radiating (absorbing) Dy atom
z
⇒ lineshape broadening and shift
Collisional effects in high-vacuum (10-6 Torr) have
rarely been measured
z
z
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 Data
235 MHz
100
100
80
80
y = -1.61 (2) x + 115 (1)
60
ν 0 - 234 661 000 (Hz)
3.1 MHz
60
40
40
20
20
0
0
-20
-20
-40
-40
-60
-60
y = 1.63 (4) x - 119 (2)
-80
-80
-100
0
10
20
30
40
50
60
70
N2 Pressure (μ Torr)
80
90
-100
100
ν 0 - 3 074 000 (Hz)
Collisional Shifts due to N2
Collisional Shifts
Gas
Shift Coefficients (Hz/μTorr)
3.1-MHz
235-MHz
H2
-0.09 (8)
-0.02 (4)
He
-1.27 (6)
+1.25 (3)
Ne
-0.02 (6)
-0.01 (3)
N2
+1.72 (7)
-1.71 (5)
O2
<5
Ar
+2.14 (11)
-2.21 (7)
Kr
+2.78 (9)
-2.78 (7)
Xe
+2.75 (10)
-2.74 (7)
-1.97 (30)
Conclusion:
⇒ collisional effects are consistent with those found
in 1-Torr measurements
z
Laser Detuning Effect
Laser Detuning Effect for 754-MHz Transition
Signal (arb. units)
600
200
-200
-600
ν ο - 753 513 000 (Hz)
1000
-1000
-100
-80
-60
-40
-20
0
20
40
60
80
833-nm Laser Freq. (MHz)
Laser Detuning Effect for 235-MHz Transition
Signal (arb. units)
150
100
50
0
-120 -100
-80
-60
-40
-20
0
20
40
833-nm Laser Freq. (MHz)
60
80
100
ν o - 234 661 000 (Hz)
200
Results
-0.6 ± 6.5 Hz/yr
.
α/α = (-0.3 ± 3.6) x 10-15 yr-1
9.0 ± 6.7 Hz/yr
(-5.0 ± 3.7) x 10-15 yr-1
Result: Phys. Rev. Lett. 98, 040801 (2007)
.
α/α = (-2.9 ± 2.6mostly syst) x
10-15
yr-1
Independent of other
fundamental constants
The Future

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