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