Atom Interferometry

Prof. Mark Kasevich Dept. of Physics and Applied Physics

Stanford University, Stanford CA

Young’s double slit with atoms

Young’s 2 slit with Helium atoms

Slits

Interference fringes

One of the first experiments to demonstrate de Broglie wave interference with atoms, 1991 (Mlynek, PRL, 1991)

Simple models for inertial force sensitivity

Gravity/Accelerations

g

(longer de Broglie wavelength)

As atom climbs gravitational potential, velocity decreases and wavelength increases

Rotations Sagnac effect for de Broglie waves

Current ground based experiments with atomic Cs: Wavepacket spatial separation ~ 1 cm Phase shift resolution ~ 10–5 rad

(Previous experiments with neutrons)

Resonant traveling wave optical excitation, (wavelength λ)

(Light-pulse) atom interferometry

2-level atom

|2〉

|1〉

Resonant optical interaction

Recoil diagram

Momentum conservation between atom and laser light field (recoil effects) leads to spatial separation of atomic wavepackets.

Laser cooling

Laser cooling techniques are used to achieve the required velocity (wavelength) control for the atom source.

Laser cooling: Laser light is used to cool atomic vapors to temperatures of ~10-6 deg K.

Image source:www.nobel.se/physics

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 (April 2002) also App. Phys. B, 2006.

Gyroscope

Measured gyroscope output vs.orientation:

Typical interference fringe record:

•  Inferred ARW: < 100 µdeg/hr1/2

•  10 deg/s max input •  <100 ppm absolute accuracy

Measurement of Newton’s Constant

Pb mass translated vertically along gradient measurement axis.

Yale, 2002 (Fixler PhD thesis)

Characterization of source mass geometry and atom trajectories (with respect to source mass) allows for determination of Newton’s constant G. Use gravity gradiometer to reject spurious technical vibrations.

Measurement of G

Systematic error sources dominated by initial position/velocity of atomic clouds. δG/G ~ 0.3%

Fixler, et al., Science, 2007, also Fixler PhD thesis, 2003.

Differential accelerometer

Applications in precision navigation and geodesy

~ 1 m

Gravity gradiometer

Demonstrated accelerometer resolution: ~10-11 g.

Truck-based gravity gradient survey (2007)

ESIII loading platform survey site

Gravity gradient survey

Gravity anomally map from ESIII facility

Gravity gradient survey of ESIII facility

Test Newton’s Inverse Square Law

Using new sensors, we anticipate δG/G ~ 10-5.

This will also test for deviations from the inverse square law at distances from λ ~ 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 µK to enforce tight control over kinematic degrees of freedom

Statistical sensitivity

δg ~ 10-15 g with 1 month data collection

Systematic uncertainty δg ~ 10-16 limited by magnetic field inhomogeneities and gravity anomalies.

Also, new tests of General Relativity

10 m atom drop tower

Atomic source

10 m drop tower

atom

laser

Post-Newtonian Gravitation

Light-pulse interferometer phase shifts for Schwarzchild metric:

•  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.

Collaborators: Savas Dimopoulos, Peter Graham, Jason Hogan.

Atom and photon geodesics

Parameterized Post-Newtonian (PPN) analysis Schwazchild metric, PPN expansion:

Corresponding AI phase shifts:

Projected experimental limits:

Steady path of apparatus improvements include:

•  Improved atom optics (T. Kovachy)

•  Taller apparatus

•  Sub-shot noise interference read-out

•  In-line, accelerometer, configuration (milliarcsec link to external frame NOT req’d).

(Dimopoulos, et al., PRL 2007)

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 δg ~ 10-16 g level.

(Hogan, Johnson, Proc. Enrico Fermi, 2007)

Equivalence Principle Installation

Gravity Wave Detection

Distance between objects modulates by hL, where h is strain of wave and L is their average separation.

Interesting astrophysical objects (black hole binaries, white dwarf binaries) are sources of gravitational radiation in 0.01 – 10 Hz frequency band.

LIGO is existing sensor utilizing long baseline optical interferometry. Sensitive to sources at > 40 Hz.

Gravity waves

Metric (tt):

Differential accelerometer configuration for gravity wave detection.

Atoms provide inertially decoupled references (analogous to mirrors in LIGO)

Gravity wave phase shift through propagation of optical fields. 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).

Satellite configuration (dashed line indicates atom trajectories)

Satellite Configuration

Lasers, optics and photodetectors located in satellites S1 and S2.

Atoms launched from satellites and interrogated by lasers away from S1 and S2.

Configuration is free from many systematic error sources which affect proposed sensors based on macroscopic proof masses.

Stochastic Sources/Satellite exp’t

White dwarft

Terrestrial Sensor

DUSEL facility: 1 km vertical shaft at Homestake mine. In the future, deeper shafts may be available.

1 km

Seismic Noise

Seismic noise induced strain analysis for LIGO (Thorne and Hughes, PRD 58) .

Seismic fluctuations give rise to Newtonian gravity gradients which can not be shielded.

Primary disturbances are surface waves. Suggests location in underground facility.

(Possible) DUSEL Installation

Collaboration with SDSU, UofTenn, NASA Ames to install protoptype sensor.

Also, next generation seismic sensors (John Evans, USGS).

Sub-surface installation may be sufficiently immune to seismic noise to allow interesting ground-based sensitivity limits.

(data courtesy of Vuk Mandic, UofM)

Cosmology

Are there (local) observable phase shifts of cosmological origin?

Analysis has been limited to simple metrics: –  FRW: ds2 = dt2 – a(t)2(dx2+dy2+dz2) –  McVittie: ~Schwarzchild + FRW

No detectable local signatures for Hubble expansion (shift ~H2)

Interesting phenomenology from exotic/speculative theories?

Giulini, gr-qc/0602098

Future

1)  Wavepackets separated by z = 10 m, for T = 1 sec. For Earth gravity field: Δφ ~ mgzT/ ~ 2x1011 rad

2)  Signal-to-noise for read-out: SNR ~ 105:1 per shot. (squeezed state atom detection, 108 atoms per shot)

3)  Resolution to changes in g per shot: δg ~ 1/(Δφ SNR) ~ 4x10-17 g

4)  106 shots data collection: δg ~ 4x10-20 g (!)

How do we exploit this sensitivity?

Towards macroscopic quantum interference

Δφ ~ mgzT/ Gravitational phase shift scales linearly with mass of interfering particle (quasi-particle).

Therefore, improved sensitivity with increased mass for interfering particle.

How? Molecules, C60, etc. Nanostructures QND correlated many-body states Weakly bound quasi-particles

Possible interference with >106 amu objects. Entanglement via gravitational interaction?

Fundamental limits?

Are there fundamental limits?

Penrose collapse Non-linearity in quantum mechanics Space-time fluctuations (eg. due to Planck–scale fluctuations)

In coming years, AI methods will provide a >106-fold improvement in sensitivity to such physics.