BEC Interferometry and Applications - University of … · BEC Interferometry and Applications ......
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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 ~ Et i e ψ - 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 1 U 0 2 2 Split 2 U Split 0 = + +- = = 2, 2, 0 + - 2 2 0 N Split cos N 2 φ = φ = φ k p k p ℏ ℏ 2 moving 2 2 moving 2 rest at 0 - = - + = + 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 . t s = 24 μs t s = 24 μs t w = 33 μs 3.03 ω r 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 6 0.0 0.2 0.4 0.6 0.8 1.0 N 0 /N I·t [mW ms cm -2 ] It c 0 2 ε α φ ℏ = Δ α = polarizability I = intensity t = pulse time Measure α at Δ = 6.6 GHz, 13 THz 6% accuracy DC Polarizability Sagnac m 4A Δφ = π •Ω ℏ ℏ t E DC 2 2 1 α φ = Δ 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 0 N N
Transcript of BEC Interferometry and Applications - University of … · BEC Interferometry and Applications ......
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
