using the fine structure constant to push on the...

Lecture 5: Using the Fine Structure Constantto Push on the Standard Model

The 64th Compton Lecture Series

Unsolved Mysteries of the Universe:Looking for Clues in Surprising Places

THE ENRICO FERMI INSTITUTE

Brian Odom

http://kicp.uchicago.edu/~odom/compton.htm

Oct. 21, 2006 Brian Odom Compton Lecture 5

The Fine Structure Constant2e

cα =

2P

1S

2P

1S

Hydrogen Energy Levels

Predicted Emission Spectrum

If there were no fine structure

With fine structure

10.2 eV (121.6 nm)10.2 eV (121.6 nm)

4.5 x 10-5 eV


Coupling Constants

The fine structure constant quantifies the strength of the coupling of light to matter, or the strength of electromagnetism.

We will talk only aboutthe low-energy limit


What is its Value?

“It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.”

- Richard Feynman

It is “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man."

- Richard Feynman

Despite many attempts, α remains one of the free parameters of the standard model. We cannot predict it; we must measure it.


What is its Value?

1137

α ≈

…but not quite

1 137α − ≈or

1 137.035 999 710 (96)α − ≈Gabrielse, Hanneke, Kinoshita, Nio, and Odom, Phys Rev Lett 97, 030802 (2006)


A Good Thing that it is Small1 1

137α ≈

1st order:

This allows us to use perturbation theory for calculations

2nd order:

3rd order:

+ +

+ …


Old Quasar Light…Is it Really Constant?

Murphy, et. al. Mon. Not. R. Astron Soc. 345 (2003)

( figure from Chris Churchill )


Old Quasar Light…Is it Really Constant?

figure from Chris Churchill

Srianand, et al. Phys. Rev. Lett.. 92, 12 (2004)

… systematics errors can be tricky


Is it Really Constant?

α αΔzexperiment α α≈ (yr -1)

< 6 x 10-17< 6 x 10-70.4 – 2.3QSO absorp., Srianand et. al.64 (14) x 10-17

< 20 x 10-17< 0.5 x 10-17< 200 x 10-17

54 (12) x 10-70.5 – 3.5QSO absorp., Murphy et. al.

< 8 x 10-70.45Meteorite Re/Os abundance< 0.1 x 10-70.14Oklo nuclear phenomenon< 6 x 10-150Lab atomic transitions (Yb/Cs)


< 20 x 10-17< 0.5 x 10-17< 200 x 10-17



So far, there is no evidence that α varies with time. But, it does vary in some theories. …We keep looking.

(…but I heard yesterday that the lab results have improved substantially)

An interesting note: these experiments have fantastic sensitvity to variations of α, but they are not the best ways to measure its actual value


Electron Magnetic Moment

If the electron is a point particle (has no size), the Standard Model allows precise prediction of the magnetic moment, provided we know α

0th order:

1st order: + …


The g - Factor

Classical, non-relativistic

Dirac equation as single-particle wave equation

Quantum Electrodynamics (QED)

2.002 319 304g = ...

2g =

1g =

2q S

gm

μ⎛ ⎞

= ⎜ ⎟⎝ ⎠


Why Measure the g - Factor?

• Determination of α, using QED calculations

• Precision test of QED

• Probe for electron sub-structure

• Precision test of Lorentz, CPT symmetry

• Complement to the muon g – factor measurement

(which is a great search for new particles)

• Prospects for improved proton to electron mass

ratio


Does the Electron Have Size?

So far we have no reason to believe it has size… but we keep looking.


Testing Quantum Electrodynamics

α-1137.03599 137.03600 137.03601

Δα / α (ppb)-100-50050100

muonium h.f. structure

electron g, UW 1987

quantum Hall effect

ac Josephson effect & γp,h

h / mn

h / mCs, optical transitions, mass ratios

electron g, Harvard 2006

h / mRb, mass ratios


Different Levers for New Physics

α αΔzexperiment α α≈ (yr -1)


< 20 x 10-17< 0.5 x 10-17< 200 x 10-17




< 20 x 10-17< 0.5 x 10-17< 200 x 10-17



Some people use high precision over short times. Some people use enormous times and less precision.

(…but I heard yesterday that the lab results have improved substantially)


Different Levers for New Physics

Higher energy means shorter wavelength—and the ability to look for even smaller structure

… or we can do precision measurements, like measurement of the g - factor


g from the Standard Model2 3 4

1 2 3 41 ...2g C C C C non QEDα α α α

π π π π⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + + + + + + −⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠


An Electron in a Penning Trap

B Field E Field magnetronmotion

axialmotion

cyclotronmotion

0.02 Hz7.2 K149.0 GHzcyclotron

10-17 Hz6.4 μK130 kHzmagnetron

10-12 Hz7.2 K149.2 GHzspin

1 Hz9.6 mK200 MHzaxial

dampinghυ/kbfrequencymotion


Do a Frequency Measurement!

( )( ) ( )

2 1a z c 2

21 1c z c2 2

2=1

2 2g ω ω ω δ

ω δ ω ω δ− +

++ + +

s

c2g ω

ω=

g in free space:

g-2 in free space:

a

c

21 12 2g g ω

ω−= + = +

g-2 in a Penning trap:

[ Brown and Gabrielse. Rev. Mod. Phys. 58, 1 (1986) ](3 orders of magnitude for free)

2q S

gm

μ⎛ ⎞

= ⎜ ⎟⎝ ⎠

Definition:


Cylindrical Penning Trap Construction


Dilution Refrigerator and Magnet

10'1"

x10


The Lab


A tabletop experiment …if you have a high ceiling


Detection of a Single Electron•The axial oscillator is coupled to a tuned-circuit amplifier

Signal Out

−20 −10 0 10 20

0.0

0.4

ampl

itude

(a. u

.)

−20 −10 0 10 20−0.5

0.0

0.5

frequency − νz (Hz)

•Axial motion is driven to increase signal


Single Quantum Jumps

decay time (s)0 10 20 30 40 50 60

num

ber o

f n=1

to n

=0 d

ecay

s

0

10

20

30

time (s)0 100 200 300

axia

l fre

quen

cy s

hift

(Hz)

-3

0

3

6

9

12

15τ = 16 s

•In free space, cyclotron lifetime = 0.08 s

•In our cylindrical traps, we have

achieved a 16 s lifetime

[ Peil and Gabrielse. Phys. Rev. Lett. 83, 1287 (1999) ]


Benefits of Cooling Down

Relativistic Corrections

•Eliminates relativistic errorfrom ωc uncertainty

Thermal Jumps4.2 K

012

3.2 K

012

2.0 K

012

1.6 K

012

.08 K

time (minutes)0 5 10 15 20 25 30 35 40 45 50

cycl

otro

n qu

antu

m n

umbe

r

012

[ Peil and Gabrielse. Phys. Rev. Lett. 83, 1287 (1999) ]

•Reducing thermal jumps permits single-quantum cyclotron spectroscopy


T-Dependent Magnetism…BAD

An unpleasant surprise:

•We observed a huge shift of B-field vs. trap temperature

•Heat load changes are unavoidable as:

•Amplifier cycles on/off

•Anomaly drive is applied

•10 ppb / mK is far too much!

tem

pera

ture

(mK

)

707580859095

100105

time (hours)0 2 4 6 8 10

B fi

eld

shift

(ppb

)

-300-250-200-150-100

-500

Shift of -10 ppb / mK at 75 mK !!!


It’s the Trap!

temperature (Kelvin)

0.0 0.5 1.0 1.5 2.0

mag

netic

fiel

d sh

ift (p

pb)

-100

0

100

200

300

400

500

600

700

temperature-1 (Kelvin-1)

0 5 10 15-100

0

100

200

300

400

500

600

700

•Nuclear paramagnetism makes standard Penning trap materials (copper, MACOR) incompatible with a stable B-field below 1 K


New Silver Trap


Prototype Silver Tripod


Silver Trap Improvement

temperature (Kelvin)

0.0 0.5 1.0 1.5 2.0

mag

netic

fiel

d sh

ift (p

pb)

-100

0

100

200

300

400

500

600

700

copper trapsilver trap

temperature-1 (Kelvin-1)

0 5 10 15-100

0

100

200

300

400

500

600

700

copper trapsilver trap

0.0 0.5 1.0 1.5 2.0

expa

nded

200

x

-10

0

10

20

30

•New silver trap decreases T-dependence of the field by ~ 400•With the silver trap, sub-ppb field stability is easily achieved


More Benefits of Cooling Down

frequency - 146 832 090.270 kHz-0.5 0.0 0.5 1.0 1.5

quan

tum

jum

p fr

actio

n

0.00

0.05

0.10

0.15

0.20

2 ppb

frequency - 146 832 090.270 kHz-4 -2 0 2 4 6 8

quan

tum

jum

p fr

actio

n

0.00

0.05

0.10

0.15

0.20

10 ppb

Harvard cyclotron line

[ Van Dyck et al., QED, Kinoshita, ed. 1990]

101500150B2 (T/m2)

200

0.6

Harvard

0.09

0.1

60υz (MHz)

6Tz (K)

U. Wash. H

UW

ΔΔ

H

UW0.09Δ

Δ =


Scatter of Measurements

uWave power (a.u.)0 20 40 60 80

176

178

180

182

184

186

UW 1991

uWave power (a.u.)0 20 40 60 80

176

178

180

182

184

186

Harvard 2006UW 1987


Cavity Shift Systematic

• Parametric response of large e- cloud maps cavity mode structure

• Modes coupling to centered single e- cloud are easily identified[ Tan and Gabrielse. App. Phys. Lett. 55, 2144 (1989) ]

TE1n1TM1n1


Lifetime Shifts

Q = 6500E

Q = 1400M

• Perform single e- experiments between TE127 and TM143

• Cyclotron lifetime data shows qualitatively correct behavior

• Fixing mode ω s and fitting for Qs gives reasonable results


Apparent g – Factor Shift


And the Number is …Harvard g-factor measurement:• Fully quantum measurement eliminates relativistic shift

( 1 ppt per quantum level )

• Low temperature allows quantum spectroscopy and narrows lines

• Cylindrical trap allows first quantitative treatment of cavity shift

g / 2 = 1.001 159 652 180 85 (76)(0.76 ppt)

α = 137.035 999 710 (90) (32)137.035 999 710 (96)

(0.70 ppb)

-1

Results :


New Value for α

using the fine structure constant to push on the...

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