Gravitational Physics with Atom Interferometry

Prof. Mark KasevichDept. of Physics and Applied Physics

Stanford University, Stanford CA

Atom interferometric inertial sensors

Pulses of light are used to coherently manipulated the center-of-mass motion of atomic wavepackets

Phase shifts: Semi-classical approximationThree 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

Gyroscope output vs.orientation.

200 mdeg/hr1/2

Interior view F=3

F=4

5

Gravimeter, Measurement of g

Fabricated and tested at AOSense, Inc., Sunnyvale, CA.

Sensors designed for precision navigation.

AOSense, Inc. DARPA DSO

6

Gyroscope mode/Rotational Seismology

AOSense, Inc. DARPA DSO

+30 min

Gyroscope output necessary to disambiguate tilt from horizontal motion (navigation problem).

Honduras/offshore 7.3

Differential accelerometer

Applications in precision navigation and geodesy

~ 1 m

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 ModelUse 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

Related work: Howell, PRL 102, 173601 (2009); Howell, Phys. Rev. A 81, 033813 (2010).

~ 1 prad/Hz1/2 performance achieved

Angle pick-off:Optical lever + Sagnac interferometer for precision angle measurement

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 beam-steering axis achieved by controlling orientation of retro-reflecting mirror.

Top view of mirror

Magnetic shields

Magnetic shielding specifications require joint-free shields over 10 m.

Achieved 100 mG axial uniformity over 10 m.

Shields at annealing facility

atom

laser

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.

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.

Atom and photon geodesics

Tests of General RelativitySchwarzschild metric, PPN expansion:

Corresponding AI phase shifts:

Projected experimental limits:

Steady path of apparatus improvements include:

• Improved atom optics

• Longer baseline• Sub-shot noise

interference read-out

(Dimopoulos, et al., PRL 2007; PRD 2008)

Gravity waves

Atoms provide inertially decoupled referencesGravity wave phase shift through propagation of optical fieldsEvades quantum measurement noise (photon scattering regularized by non-linear 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 co-workers)

Considering ISS, free-flyer LEO configurations

Possible instrument configuration

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.

Error models

Wavefront distortion: temporal variationsTime varying wavefront inhomogeneities will lead to non-common 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

See also, P. Bender, to be published.

J. M. Hogan, et al., 1009.2702 (2010), submitted; arXiv.

Atom cloud kinematic constrainsShot-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

See also, P. Bender, to be published.

J. M. Hogan, et al., 1009.2702 (2010), submitted, arXiv

Acknowledgements– 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