Measuring Polarizability with an Atom Interferometer

Melissa Revelle

Overview

The Importance of Atomic Polarizability

Our Interferometer Modeling the

Experiment Progress Future

Why Atomic Polarizability?

Relates to Van der Waals forces Black body shifts for

atomic clocks Depths of optical

dipole traps for atoms

Precision of αNa = 0.5% Precision of αK = 2%

Ep

E

p p

Using Phase Shift to Find Polarizability

Atom beam Detector

1G

v2

2xE

2G 3G

Using Phase Shift to Find Polarizability

Atom beam Detector

1G

v2

2xE

x

2G 3G

Using Phase Shift to Find Polarizability

Atom beam Detector

1G

v2

2xE

x

2G 3G

Original Data

Atom flux at each grating position is recorded Polarizability relates to this phase shift

Phase Shifts in an Atom Interferometer

From the Schrödinger equation for an atom beam, we get:

The total phase shift becomes:

))((2

)(xUTm

xk

1

)(v2

21 dxxE

The Electric Field Gradient Region

x

y

Atom beams

y

x

z

The Electric Field Gradient Region

x

y

y

x

z

Finding the Equipotential Surfaces and Charge Density For an ideal wire and

an image wire:

22

22

0 )(

)(ln

2 xyd

xydV

o

g

d

y0 R

y

x

z

Atom beams

Creating the Model

Integrate along a path in the x direction to get the phase shift.

L=distance from 1G to gradient region

a=grating period

mam

Lhs 55

v

v))v(cos()v(

v))v(sin()v(arctan

dP

dP

Fitting the Data

The model for the E-field and phase shift is used as a fit function

Distance from Cylinder [mm]

Ph

ase

Sh

ift

[rad

]

Data

Fit Function

Summary

We can precisely measure polarizability using atom interferometry.

The electric field must be accurate.

Velocity distribution is important

Current and Future Progress

Improve precision polarizability of sodium and potassium to better than 1%

Measure the polarizability tensor components of molecules.

1.08.23 Na4.00.43 K

References

A.Salop, E. Pollack, and B. Bederson, Phys. Rev. 124, 1431 (1961)

L. de Broglie, Ann. Phys. (Paris) 3, 22 (1925)

R. Molof, H. Schwartz, T. Miller, and B. Bederson, Phys. Rev. A 10, 1131 (1974)