BEC Interferometry and Applications Robert Horne, Bob Leonard, and Cass Sackett

Atom Interferometry • Manipulate atomic wave functions

• Measure phase

• Measurement of gravity, inertial effects, atomic properties

Advantages of Condensates

• Easier to control – permit “guided wave” interferometers

• Hope for more flexible trajectories, longer interaction times

• Support atoms against gravity - shorter apparatus

• Coherent waves means high contrast

~Eti

eψ−

ℏ

x y

z

Waveguide

• Supports atoms against gravity and provide spatial confinement

• Harmonic confinement:

Weak Longitudinal Confinement Reduces Noise • Lower density – weaker atomic interactions

• Energy differential across wave packet

x

y

z

/ 2 5.7 Hz

/ 2 0.21 Hz

/ 2 3.3 Hz

ω π =

ω π =

ω π =

y∝ ω

Symmetric Trajectory • Phase φ = φ(y), varies across packet

• Symmetric interferometer cancels the effect of these gradients

Recombination & Phase Extraction • Overlapping atoms have inference fringes too small to resolve

• The split pulse acting on & gives:

• For a phase shifted wave function, , we find

the number of atoms coming to rest by:

( ) Split

Split

1U 0 2 2 Split

2

U Split 0

= + + − =

=

2 , 2 , 0+ −

2 20N Split cosN 2

φ = φ =

φ

kp

kp

ℏ

ℏ

2moving2

2moving2

restat0

−=−

+=+

2− 2+0

Split & Reflect Beam • The atoms achieve spatial separation via

pulses of off-resonant light

• This light forms a standing wave which acts

similar to an optical diffraction gating

• Split operation is a two photon process

involving an absorption and stimulated emission

• The same beam reverses the motion of the atoms

by driving them from .

ts = 24 µs t

s = 24 µs

tw

= 33 µs

3.03 ωr

Split Pulse:

0 T/4 3T/4 T

Position (y)

Time

Measurements

AC Polarizability (AC Stark Shift) • Shine laser on one packet • Measure induced phase

0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

N0/N

I·t [mW ms cm-2]

Itc 02 ε

αφ

ℏ=∆

α = polarizability I = intensity t = pulse time

Measure α at ∆ = 6.6 GHz, 13 THz 6% accuracy

DC Polarizability Sagnac

m4 A∆φ = π • Ωℏ

ℏ

tEDC

2

2

1 αφ =∆

V

y

x

Current & Future Work

0 T/4 3T/4 T

Position (y)

Time

Dual Interferometer

• Noise from vibrations currently limit visibility

• Vibrations will couple to both interferometers in a dual setup

2 2+ ↔ −

Imaging

• is determined by

absorption imaging

• Atoms absorb resonant light, casting a

shadow which we image on a CCD camera

0N

N