Precision Precision αα Measurement: Measurement: Atom Recoil Method ReviewAtom Recoil Method Review

Victor AcostaVictor Acosta

Physics 250: Atomic PhysicsPhysics 250: Atomic Physics

Prof. Dima BudkerProf. Dima Budker

MotivationMotivation

αα shows up all over in EM calcs shows up all over in EM calcs

Methods using g-2 involve lengthy QED Methods using g-2 involve lengthy QED equations which undergo frequent revisionequations which undergo frequent revision

Working Toward an Electronic Kilogram…Working Toward an Electronic Kilogram…

Electronic KgElectronic Kg

me 2R h

c2

• Balance Gravity Force with EMF• Find value for h, Planck’s Constant•Deduce me from:

Physical Constant Uncertainties:Physical Constant Uncertainties:

Constant Relative UCppbR 0.007mpme

0.4

3.3e 85h 170kB 1800G 150000

Determining Determining αα

Measuring R∞: Compare transition frequencies in Hydrogen

using frequency chain or comb. de Beauvoir et. al. Eur Phys J D 2000, Udem et. al. 1997

Measuring mp/me and MAtom/mp

2 2R hme

2Rmpme

Matommp

hMatom

Penning TrapPenning Trap Hans Dehmelt, Nobel Prize 1989Hans Dehmelt, Nobel Prize 1989

2 2R mpmeMatommp

hMatom

Sub ppb UC for most mass ratios

2 2R mpmeMatommp

hMatom

Atom Recoil Atom Recoil Calculate Recoil Frequency Shift for Single Rb-87 Photon Absorption

Eh

p2

2MRb h h2

2MRbc2

hMRb

2c22

~10 kHz

So for ppb UC, we need μHz sensitivity!

Chu: Atom InterferometerChu: Atom Interferometer

• Use 4 π/2 Raman pulses• Creates 2 Atom Interferometers•Sensitivity Limited by Phase number of photon Recoils…

Chu’s Clever TrickChu’s Clever Trick

Adding N (here N=2) π-pulses allows for N times greater recoil shift.

ResultsResults

7.7 ppb UC7.7 ppb UC

ProblemsProblems Recoil Efficiency = 94%Recoil Efficiency = 94%

Allows other Zeeman sublevels to be populatedAllows other Zeeman sublevels to be populated

NNrecoilrecoil<60<60

Clade: Bloch Oscillations in Optical Clade: Bloch Oscillations in Optical LatticeLattice

1.1. Laser Cooling in a MOT down to 3 mK, Laser Cooling in a MOT down to 3 mK,

2.2. As in Chu expt, there is a As in Chu expt, there is a ππ pulse pulse pumping atoms of particular velocity pumping atoms of particular velocity class into F=1, class into F=1,

3.3. Force N Bloch Oscillations using Optical Force N Bloch Oscillations using Optical Lattice to build up atom recoil momentumLattice to build up atom recoil momentum

4.4. Another Another ππ pulse tuned to F=1 -> F'=2 to pulse tuned to F=1 -> F'=2 to measure final velocity via TOF. measure final velocity via TOF.

Bloch Oscillations: Tilted LatticeBloch Oscillations: Tilted Lattice

Marble would fall (classically), but atom-waves oscillate!Marble would fall (classically), but atom-waves oscillate!Periodicity of Bloch solutions requires the oscillationsPeriodicity of Bloch solutions requires the oscillations

k 2

d k and

vk 1

kk, then

vk 2

d vk. But since

kt ko F

t, then the velocity must actually be bounded in time and thus oscillatory.

Creating the Constant ForceCreating the Constant Force

Could use gravity or E-fieldCould use gravity or E-field These are undesirableThese are undesirable

Solution: Sweep the frequency of one of Solution: Sweep the frequency of one of the lasers in the Standing Wave!the lasers in the Standing Wave! Wave only “stands” in accelerated reference Wave only “stands” in accelerated reference

frameframeThink of nodes/antinodes moving accelerating Think of nodes/antinodes moving accelerating down the line as the frequency is sweptdown the line as the frequency is swept

ApparatusApparatus

ResultsResults

6.7 ppb (Chu 7.7 ppb)6.7 ppb (Chu 7.7 ppb) g-2 record is 3.9 ppb, Gabrielse et. al.g-2 record is 3.9 ppb, Gabrielse et. al.

Recoil Efficiency: 99.7% (Chu 94%)Recoil Efficiency: 99.7% (Chu 94%)

NNrecoilrecoil ~ 900 (Chu 60) ~ 900 (Chu 60)