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