Precision atom interferometry
in a 10 meter tower
ICOLS 2013
Jason Hogan
Stanford University
June 11, 2013
Light Pulse Atom Interferometry
•
1D (vertical) atomic fountain
•
•
Atom is freely falling
•
Lasers pulses are atom beamsplitters &
mirrors (Raman or Bragg atom optics)
pulse sequence
Inertial Force Sensitivity
Atom-Light interaction:
The local phase of the laser is imprinted on the atom at each interaction point.
Laser phase encodes the atom’s
position as a function of time
Motion of the atom is measured
w.r.t. a wavelength-scale “laserruler” (~0.5 micron)
Example: Free-fall gravitational acceleration, (p/2 – p – p/2) sequence
Df = (fD – fB) – (fC – fA)
~
/l
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)
Ultra-cold atom source
BEC source in TOP trap, then diabatic steps in strength of
trap to further reduce velocity spread:
< 3 nK
Atom cloud imaged after 2.6 seconds free-fall
No apparent heating from lattice launch
Interference at long interrogation time
Wavepacket separation at
apex (this data 50 nK)
2T = 2.3 sec
Near full contrast
6.7×10-12 g/shot (inferred)
Interference (3 nK cloud)
Dickerson, et al., arXiv:1305.1700 (2013)
Phase shifts: semi-classical approximation
Three contributions to interferometer phase shift:
Propagation
shift:
Laser fields
(Raman
interaction):
Wavepacket
separation at
detection:
Storey and CCT, J. Physique II, 1994;
Bongs, et al., App. Phys. B, 2006.
Phase shifts
Gravity
Coriolis
Timing asymmetry
Curvature, quantum
Gravity gradient
Wavefront
(Tij, gravity gradient; vi, velocity; xi, initial position; a, wavefront
curvature; g, acceleration; T, interrogation time; keff, effective
propagation vector)
Observe velocity dependent shifts with spatial imaging
(useful when atoms expand from a point source)
Coriolis phase shift
Side
view
Coriolis phase shift:
Expansion from point source:
No gradient
Phase gradient
F=2
F=1
F=2
F=1
Top
view
Measurement Geometry
Dickerson, et al., arXiv:1305.1700 (2013)
Coriolis phase shift
Side
view
Coriolis phase shift:
Expansion from point source:
No gradient
F=1
Phase gradient
F=1
Top
view
F=2
F=2
Measurement Geometry
Dickerson, et al., arXiv:1305.1700 (2013)
2-axis rotation measurement
Interference patterns for rotating platform:
Side
view
2-axis gyroscope
Top
view
Measurement Geometry
Measurement of rotation rate near null rotation
operating point.
Dickerson, et al., arXiv:1305.1700 (2013)
Phase shear readout
Tilt angle of final pulse to introduce a phase shear 
Enables simultaneous read-out of contrast and phase
Sugarbaker, et al., arXiv:1305.3298 (2013).
Phase shear readout
Phase Shear Readout (PSR)
F=2
(pushed)
F=1
g
F=1
g
F=2
(pushed)
1 cm
1 cm
≈ 4 mm/s
Mitigates noise sources:
 Pointing jitter and residual rotation readout
 Laser wavefront aberration in situ characterization
Single-shot
interferometer phase
measurement
Phase shear readout
Phase Shear Readout (PSR)
F=2
(pushed)
F=1
g
F=1
g
F=2
(pushed)
1 cm
1 cm
≈ 4 mm/s
Mitigates noise sources:
 Pointing jitter and residual rotation readout
 Laser wavefront aberration in situ characterization
Single-shot
interferometer phase
measurement
Phase shear readout
Phase Shear Readout (PSR)
F=2
(pushed)
F=1
g
F=1
g
F=2
(pushed)
1 cm
1 cm
≈ 4 mm/s
Mitigates noise sources:
 Pointing jitter and residual rotation readout
 Laser wavefront aberration in situ characterization
Single-shot
interferometer phase
measurement
Phase shear readout
Phase Shear Readout (PSR)
F=2
(pushed)
F=1
g
F=1
g
F=2
(pushed)
1 cm
1 cm
≈ 4 mm/s
Mitigates noise sources:
 Pointing jitter and residual rotation readout
 Laser wavefront aberration in situ characterization
Single-shot
interferometer phase
measurement
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.
Equivalence Principle
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.
General relativistic phase shifts
Light-pulse interferometer
phase shifts in GR:
• Geodesic propagation
for atoms and light.
• Path integral
formulation to obtain
quantum phases.
• Atom-field interaction
at intersection of laser
and atom geodesics.
laser
atom
Atom and photon geodesics
Prior work, de Broglie interferometry: Post-Newtonian effects of gravity on quantum
interferometry, Shigeru Wajima, Masumi Kasai, Toshifumi Futamase, Phys. Rev. D, 55,
1997; Bordé, et al.
Tests of General Relativity
Schwarzschild metric, PPN expansion:
Steady path of
apparatus
improvements
include:
Corresponding AI phase shifts:
• Improved atom
optics
• Longer baseline
• Sub-shot noise
interference readout
Projected experimental limits:
(Dimopoulos, et al., PRL 2007; PRD 2008)
Gravitational Wave Detection
frequency
L (1 + h sin(ωt ))
Megaparsecs…
strain
Why study gravitational waves?
• New carrier for astronomy: Generated by moving mass instead of electric charge
• Tests of gravity: Extreme systems (e.g., black hole binaries) test general relativity
• Cosmology: Can see to the earliest times in the universe
But, they are incredibly weak!
• Strain oscillation: Amplitude of motion depends on separation
• Example: 1000 km baseline, oscillation amplitude is only 10 fm
Gravitational Wave Detection
Why consider atoms?
• Neutral atoms are excellent “test particles” (follow geodesics)
• Atom interferometry provides exquisite measurement of geodesic
• Single baseline configuration possible (e.g., only two satellites)
• Comparable sensitivity to LISA, but much smaller (1000 x)
• Flexible operation modes (broadband, resonant detection)
Satellite GW Antenna
Atoms
Common interferometer laser
Atoms
L ~ 1000 km
• Atoms are test masses
• Atom is inertially decoupled (freely
falling); insensitive to vibration
• Gravity wave phase shift through
propagation of optical fields
• Differential measurement with
common laser helps suppress noise
Potential strain sensitivity
J. Hogan, et al., GRG 43, 7 (2011).
Technology development for GW detectors
1) Large wavepacket separation (meter scale)
2) Ultra-cold atom temperatures (picoK)
3) Spatial wavefront noise characterization
4) Laser frequency noise mitigation strategies
Large momentum transfer atom optics
Chiow, PRL, 2011
102 photon recoil atom optics
0.6 m/sec recoil
Large momentum transfer atom optics
Sequence of 6hk Bragg pulses used to realize a
102hk atom interferometer.
Sample
interferometer
pulse sequence
Scalable to 1000 hk?
LMT with long interrogation time
6 ħk sequential Raman in 10 meter tower
2T = 2.3 seconds
4 cm wavepacket separation
Two-photon vs. single photon configurations
1 photon transitions
2-photon transitions
Rb
GW signal from relative positions of
atom ensembles with respect to
optical phase fronts.
Sr
GW signal from light propagation
time between atom ensembles.
Laser frequency noise insensitive detector
• Long-lived single photon
transitions (e.g. clock
transition in Sr, Ca, Yb, Hg,
etc.).
• Atoms act as clocks,
measuring the light travel
time across the baseline.
• GWs modulate the laser
ranging distance.
Excited
state
Laser noise
is common
Graham, et al., arXiv:1206.0818, PRL (2013)
Laser frequency noise insensitive detector
Example LMT beamsplitter (N = 3)
• Long-lived single photon
transitions (e.g. clock
transition in Sr, Ca, Yb, Hg,
etc.).
• Atoms act as clocks,
measuring the light travel
time across the baseline.
• GWs modulate the laser
ranging distance.
Graham, et al., arXiv:1206.0818, PRL (2013)
Kinematic noise sensitivity
Laser noise cancels. What are the remaining sources of noise?
Relative velocity Δv between the interferometers changes the time
spent in the excited state, leading to a differential phase shift.
Leading order kinematic noise sources:
1. Platform acceleration noise da
2. Pulse timing jitter dT
3. Finite duration Dt of laser pulses
4. Laser frequency jitter dk
Most severe constraint on laser frequency noise is that laser
needs to be resonant with the transition
(linewidth < transition Rabi freq.)
AI technology progress and future work
• Large wavepacket separation
• Large Momentum Transfer (LMT) atom optics
• Ultracold atoms temperature
• Optical wavefront noise mitigation
• Phase readout
• Satellite rotation jitter mitigation
• Strontium atom interferometry development
Collaborators
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 Rudolf (Hannover)
NASA GSFC
Babak Saif
Bernard D. Seery
Lee Feinberg
Ritva Keski-Kuha