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Gravitational Physics with Atom
Interferometry
Prof. Mark Kasevich
Dept. of Physics and Applied Physics
Stanford University, Stanford CA
Atom interferometric inertial sensors
Pulses of light are used to coherently manipulated the centerof-mass motion of atomic wavepackets
Phase shifts: Semi-classical approximation
Three contributions to interferometer phase shift:
Propagation
shift:
Laser fields
(Raman
interaction):
Wavepacket
separation at
detection:
See Bongs, et al., quant-ph/0204102
(2002), also App. Phys. B, 2006.
Gyroscope, Measurement of Earth rotation rate
F=4
Interior
view
F=3
Gyroscope output vs.orientation.
200 mdeg/hr1/2
Gravimeter, Measurement of g
Fabricated and tested at
AOSense, Inc., Sunnyvale, CA.
Sensors designed for precision
navigation.
AOSense, Inc.
DARPA DSO
5
Gyroscope mode/Rotational Seismology
Honduras/offshore 7.3
+30 min
Gyroscope output necessary to disambiguate tilt from
horizontal motion (navigation problem).
AOSense, Inc.
DARPA DSO
6
Differential accelerometer
~1m
Applications in precision navigation and geodesy
Gravity gradiometer
Demonstrated accelerometer
resolution: ~10-11 g.
Test Newton’s Inverse Square Law
Using new sensors, we anticipate
dG/G ~ 10-5.
This will also test for deviations from
the inverse square law at distances
from l ~ 1 mm to 10 cm.
Theory in collaboration with S.
Dimopoulos, P. Graham, J.
Wacker.
Equivalence Principle
Co-falling 85Rb and 87Rb ensembles
Evaporatively cool to < 1 mK to
enforce tight control over kinematic
degrees of freedom
Statistical sensitivity
dg ~ 10-15 g with 1 month data
collection
Systematic uncertainty
dg ~ 10-16 limited by magnetic field
inhomogeneities and gravity
anomalies.
10 m drop tower
Error Model
Use standard methods to
analyze spurious phase shifts
from uncontrolled:
• Rotations
• Gravity
anomalies/gradients
• Magnetic fields
• Proof-mass overlap
• Misalignments
• Finite pulse effects
Known systematic effects
appear controllable at the
dg ~ 10-16 g level.
(Hogan, Johnson, Proc. Enrico Fermi,
2007)
Earth rotation compensation
Earth rotation induces
systematic phase shift which
needs to be compensated.
Strategy is to keep atom-optics
axis inertially stabilized over
interferometer pulse sequence
duration (~ 2.8 s).
Required
1 nrad angular
stability in beamsteering axis
achieved by
controlling
orientation of
retro-reflecting
mirror.
Top view
of mirror
Angle pick-off:
Optical lever + Sagnac
interferometer for precision
angle measurement
~ 1 prad/Hz1/2 performance
achieved
Related work: Howell, PRL 102,
173601 (2009); Howell, Phys.
Rev. A 81, 033813 (2010).
Magnetic shields
Shields at
annealing facility
Magnetic shielding specifications require jointfree shields over 10 m.
Achieved 100 mG axial uniformity over 10 m.
General Relativity/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)
Gravity waves
Atoms provide inertially decoupled
references
Gravity wave phase shift through
propagation of optical fields
Evades quantum measurement noise
(photon scattering regularized by nonlinear atom/photon interaction; prepare
fresh atom ensemble each shot)
Previous work: B. Lamine, et al., Eur. Phys. J. D 20,
(2002); R. Chiao, et al., J. Mod. Opt. 51, (2004); S.
Foffa, et al., Phys. Rev. D 73, (2006); A. Roura, et al.,
Phys. Rev. D 73, (2006); P. Delva, Phys. Lett. A 357
(2006); G. Tino, et al., Class. Quant. Grav. 24 (2007).
Possible satellite configuration
AGIS free-flying satellite concept
In collaboration with
GSFC (Bernie Seery,
Babak Saif and coworkers)
Considering ISS,
free-flyer LEO
configurations
Recent analysis for Earth orbiting configurations: J. M.
Hogan, D. M. S. Johnson, S. Dickerson, T. Kovachy, A.
Sugarbaker, S. Chiow, P. W. Graham, M. A. Kasevich, B. Saif,
S. Rajendran, P. Bouyer, B. D. Seery, L. Feinberg, and R
Keski-Kuha, 1009.2702 (2010), submitted.
Possible
instrument
configuration
Error models
Wavefront distortion: temporal variations
Time varying wavefront inhomogeneities will lead to noncommon phase shifts between distant clouds of atoms
- High spatial frequencies diffract out of the laser beam
as the beam propagates between atom clouds
- Limit for temporal stability of wavefronts determined
by stability of final telescope mirror
Mirror: Be at
300K
J. M. Hogan, et al.,
1009.2702 (2010),
submitted; arXiv.
See also, P. Bender, to be published.
Atom cloud kinematic constrains
Shot-to-shot jitter in the position of the atom cloud with respect to
the satellite/laser beams constrains static wavefront curvature
Wavefront
error vs.
spatial
frequency,
assuming
10 nm/Hz1/2
position jitter
J. M. Hogan, et al.,
1009.2702 (2010),
submitted, arXiv
See also, P. Bender, to be published.
Acknowledgements
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Grant Biedermann, PhD, Physics
Ken Takase, PhD, Physics
Igor Teper, Post-doctoral fellow
John Stockton, Post-doctoral fellow
Louis Delsauliers, Post-doctoral fellow
Xinan Wu, PhD, Applied physics
Jongmin Lee, Graduate student, Applied physics
Chetan Mahadeswaraswamy, PhD, Mechanical engineering
David Johnson, Graduate student, Physics
Geert Vrijsen, Graduate student, Applied physics
Jason Hogan, Post-doctoral fellow, Physics
Sean Roy, Graduate student, Physics
Tim Kovachy, Graduate student, Physics
Alex Sugarbaker, Graduate student, Physics
Susannah Dickerson, Graduate student, Physics
+ THEORY COLLABORATORS:
S. Dimopolous, P. Graham, S. Rajendran
+ GSFC COLLABORATORS:
B. Saif, B. Seery, L. Feinberg, R. Keski-Kuha
+ CNRS
P. Bouyer (See talk, MIGA terrestrial GW detector)
+ AOSENSE TEAM