precision atom interferometry in a 10 meter tower
TRANSCRIPT
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Jason Hogan Stanford University
July 20, 2013
Varenna 2013
Precision atom interferometry
in a 10 meter tower
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Gravitational wave detection
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Technology development for GW detectors
1) Long interrogation time atom interferometry
2) Large wavepacket separation (meter scale)
3) Ultra-cold atom temperatures (picoK)
4) Spatial wavefront noise characterization
5) Laser frequency noise mitigation strategies
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Light Pulse Atom Interferometry
• Lasers pulses are atom beamsplitters & mirrors (Raman or Bragg atom optics)
• pulse sequence
• 1D (vertical) atomic fountain
• Atom is freely falling
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Apparatus
Ultracold atom source >106 atoms at 50 nK
3e5 at 3 nK
Optical Lattice Launch 13.1 m/s with 2372 photon recoils to 9 m
Atom Interferometry 2 cm 1/e2 radial waist
500 mW total power
Dynamic nrad control of laser angle with precision piezo-actuated stage
Detection Spatially-resolved fluorescence imaging
Two CCD cameras on perpendicular lines of sight
Current demonstrated statistical resolution, ~5 ×10-13 g in 1 hr (87Rb)
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Ultra-cold atom source
< 3 nK
Atom cloud imaged after 2.6 seconds free-fall
No apparent heating from lattice launch
BEC source in TOP trap, then diabatic steps in strength of trap to further reduce velocity spread:
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Interference at long interrogation time
2T = 2.3 sec Near full contrast 6.7×10-12 g/shot (inferred)
Interference (3 nK cloud)
Wavepacket separation at apex (this data 50 nK)
Dickerson, et al., arXiv:1305.1700 (2013)
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Equivalence Principle Test
Co-falling 85Rb and 87Rb ensembles
Evaporatively cool to enforce tight
control over kinematic degrees of
freedom
Statistical sensitivity
dg ~ 10-15 g with 1 month data collection (2 hk atom optics)
Systematic uncertainty
dg/g ~ 10-16 limited by magnetic
field inhomogeneities and gravity
anomalies.
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Phase shifts
Observe velocity dependent shifts with spatial imaging
(useful when atoms expand from a point source)
(Tij, gravity gradient; vi, velocity; xi, initial position; a, wavefront curvature; g, acceleration; T, interrogation time; keff, effective
propagation vector)
Gravity
Coriolis
Timing asymmetry
Curvature, quantum
Gravity gradient
Wavefront
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Rotation Compensation System
nanopositioner (x3) mirror
< 1 nrad measured precision ~ 1 nrad repeatability Piezoresistive position sensors Rigidly anchored to quiet floor
In-vacuum nanopositioning stage & mirror
Anchor plate
Coarse alignment
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Observing velocity-dependent phase
Point Source Interferometry (PSI)
• Long time of flight position-velocity correlation
• Velocity-dependent phase spatial phase gradient
• Spatially resolved detection
“point source” Final size much larger than initial size
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Coriolis phase shift
Dickerson, et al., arXiv:1305.1700 (2013)
Side view
Expansion from point source:
Coriolis phase shift:
Phase gradient No gradient
F=2
F=1
F=2
F=1
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Coriolis phase shift
Dickerson, et al., arXiv:1305.1700 (2013)
Side view
Coriolis phase shift:
Phase gradient No gradient
F=2
F=1
F=2
F=1
Expansion from point source:
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Spatial fringes versus rotation rate
Interference patterns for rotating platform:
Dickerson, et al., arXiv:1305.1700 (2013)
• Spatial frequency increases with increased rotation
• Imaging the fringe pattern improves contrast
Integrated contrast
Fringe contrast
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Dual-axis gyroscope
Rotation phase shift:
CC
D2
CCD1
y
x z
CCD1:
CCD2:
Measurement of rotation rate near null rotation operating point.
Ellipse Fits CCD 1 CCD 2
F = 2 (pushed)
F = 1
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Dual-axis gyroscope
Rotation phase shift:
CC
D2
CCD1
y
x z
CCD1:
CCD2:
Precision:
Noise Floor:
CCD1
CCD2
Measurement of rotation rate near null rotation operating point.
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Phase shear readout (PSR)
g
Tilt angle of final pulse to introduce a phase shear:
Fluorescence image y
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Phase shear readout
Tilt angle of final pulse to introduce a phase shear:
Sugarbaker, et al., arXiv:1305.3298 (2013).
Enables simultaneous readout of contrast and phase
-80 µrad 0 µrad 80 µrad -40 µrad 40 µrad
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Phase shear readout
g
1 cm
F = 2 (pushed)
F = 1
≈ 4 mm/s
g
1 cm
F = 2 (pushed)
F = 1
Phase Shear Readout (PSR)
Mitigates noise sources:
Pointing jitter and residual rotation readout
Laser wavefront aberration in situ characterization
Single-shot interferometer phase measurement
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Phase shear readout
g
1 cm
F = 2 (pushed)
F = 1
≈ 4 mm/s
g
1 cm
F = 2 (pushed)
F = 1
Phase Shear Readout (PSR)
Single-shot interferometer phase measurement
Mitigates noise sources:
Pointing jitter and residual rotation readout
Laser wavefront aberration in situ characterization
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Phase shear readout
g
1 cm
F = 2 (pushed)
F = 1
≈ 4 mm/s
g
1 cm
F = 2 (pushed)
F = 1
Phase Shear Readout (PSR)
Single-shot interferometer phase measurement
Mitigates noise sources:
Pointing jitter and residual rotation readout
Laser wavefront aberration in situ characterization
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Phase shear readout
g
1 cm
F = 2 (pushed)
F = 1
≈ 4 mm/s
g
1 cm
F = 2 (pushed)
F = 1
Phase Shear Readout (PSR)
Single-shot interferometer phase measurement
Mitigates noise sources:
Pointing jitter and residual rotation readout
Laser wavefront aberration in situ characterization
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Deterministic Phase Extraction
T = 25 ms, 60 μrad misalignment at final pulse
Demonstrate single shot phase using short T interferometer
(less sensitive to seismic noise)
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Residual Coriolis
Applied shear Use PSR:
Measuring small phase shears with PSR
Alternate sign of tilt
Trial 1 Trial 2
• Applied shear adds or subtracts from residual Coriolis.
• Analogous to a heterodyne measurement in the time domain.
Can be difficult to measure small phase gradients
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Gyrocompass demonstration using phase shear
Use phase shear to determine true North
Vary rotation compensation direction, measure phase shear
0.01 deg resolution in 1 hr.
g
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PSR with timing asymmetry
δT fringes discussed earlier in lectures by E. Rasel.
(see H. Müntinga et al., PRL 2013)
-240 µs -160 µs 240 µs 160 µs 0 µs
-160 µs -80 µs 160 µs 80µs 0 µs
Beam tilt + timing asymmetry:
Vertical shear due to asymmetric pulse spacing:
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Large momentum transfer atom optics
Chiow, PRL, 2011 102 photon recoil atom optics 0.6 m/sec recoil
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LMT power requirements
• Higher Rabi frequency
• Spontaneous emission
• Larger beam diameter
Impacts temperature requirement
(Doppler broadening)
Faster transitions
More pulses/bigger LMT
Intensity uniformity impacts temperature requirement
Wavefront uniformity
Rayleigh range
Need high power lasers:
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High power laser at 780 nm
Frequency double 1560 nm fiber amplifiers in PPLN
Coherently combine two 30 W beams @ 1560 nm
S.-w. Chiow et al., Optics Letters 37, 3861 (2012)
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High power laser system for LMT in tower
• Dual output, fiber coupled
• Each output fiber gives up to 7 W at 780 nm
• Frequency control provided by phase modulation of seed light before fiber amplifiers
• Amplitude control provided by acousto-optic modulators after doubling crystals
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Wavepacket
separation at the top:
4 cm
LMT with long interrogation time
6 ħk sequential Raman in 10 meter tower
2T = 2.3 seconds
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Delta kick cooling in a harmonic trap
Harmonic Lens:
At the end of evaporation BEC:
Atom number: ~106 atoms
Cloud diameter: 10 -- 50 μm
Temperature: ~1 μK (from chemical potential)
t = 0 t < tLens t = tLens t = tLens + ε
vx
C. Monroe et al., PRL 65, 1990.
Ammann & Christensen, PRL 78, 1997
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Magnetic lens in a harmonic trap
Trap turned off
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Magnetic lens in a harmonic trap
Trap turned off
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Magnetic lens in a harmonic trap
Residual velocity is x0ω
Trap turned off
x0
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Oscillations in a TOP trap
Absorptive images of atoms released into weak TOP potential (3.7 G & 25 G/cm)
Cloud width oscillations (breathing modes) Radial Vertical
anisotropy
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Isotropic turning points in a TOP trap
Radial Vertical
TOP turn-off time
Absorptive images of atoms released into weak TOP potential (3.7 G & 22.9 G/cm)
Cloud width oscillations (breathing modes)
Tune radial and vertical trap frequencies of gravity + TOP trap using field gradient.
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Lattice Solution to Anisotropy
Lattice locks atoms vertically
z
x
Another solution: optical lattice confinement
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Lattice Solution to Anisotropy
Radial (two-dimensional) expansion
z
x x
Another solution: optical lattice confinement
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Lattice Solution to Anisotropy
Lattice turns off -- Expansion in three dimensions
z
x x x
Another solution: optical lattice confinement
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Lattice Solution to Anisotropy
Turn off trap
z
x x x x
Another solution: optical lattice confinement
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Lattice-Aided Lens Cooling
Lattice turn-off time
Cloud launched to 9 meters
20x colder (50 nK)
5 mm
TOP turn-off time
Radial
Vertical
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Extending to colder temperatures
• Delta kick in micro gravity weaker potential, more expansion
• Multiple lens sequences
• Apply additional kick at the fountain turning point?
• Apply optical potential for radial delta kick? (high power AI laser)
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Collaborators
NASA GSFC
Babak Saif
Bernard D. Seery
Lee Feinberg
Ritva Keski-Kuha
Stanford Mark Kasevich (PI)
Susannah Dickerson
Alex Sugarbaker
Sheng-wey Chiow
Tim Kovachy
Theory:
Peter Graham
Savas Dimopoulos
Surjeet Rajendran
Former members:
David Johnson Visitors:
Philippe Bouyer (CNRS) Jan Rudolph (Hannover)
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Extra
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Launch using optical lattice
Far-detuned optical standing wave potential
Velocity set by frequency difference
Coherent acceleration (negligible spontaneous emission)
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PSR phase reference
• Absolute phase depends on the path of the laser
• Atoms “illuminate” the phase prescribed by the laser sequence
Laser phase:
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• Large momentum transfer (LMT) beamsplitters – multiple laser interactions
• Each laser interaction adds a momentum recoil and imprints the laser’s phase
Example LMT interferometer LMT energy level diagram
Phase amplification factor N
LMT Beamsplitters: Coherent Phase Amplification
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AI Geometry with Large Rotation Bias
t k
0 1
T 9/4
3T 5/2
5T 9/4
6T 2
Five pulse sequence:
• Beamsplitter momenta chosen to give symmetry and closure
• Insensitive to acceleration + gravity gradients
x
z