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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. Interference fringes.

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atom interferometry

Atom Interferometry

Prof. Mark Kasevich

Dept. of Physics and Applied Physics

Stanford University, Stanford CA

young s double slit with atoms
Young’s double slit with atoms

Young’s 2 slit with Helium atoms

Interference fringes

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

Slits

simple models for inertial force sensitivity
Simple models for inertial force sensitivity

Gravity/Accelerations

Rotations

As atom climbs gravitational potential, velocity decreases and wavelength increases

Sagnac effect for de Broglie waves

(longer de Broglie wavelength)

g

Current ground based experiments with atomic Cs: Wavepacket spatial separation ~ 1 cm

Phase shift resolution ~ 10–5 rad

(Previous experiments with neutrons)

light pulse atom interferometry
(Light-pulse) atom interferometry

Resonant optical interaction

Recoil diagram

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

|2

|1

2-level atom

Resonant traveling wave optical excitation, (wavelength l)

laser cooling
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
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
Gyroscope

Measured gyroscope output vs.orientation:

Typical interference fringe record:

  • Inferred ARW: < 100 mdeg/hr1/2
  • 10 deg/s max input
  • <100 ppm absolute accuracy
measurement of newton s constant
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
Measurement of G

Systematic error sources dominated by initial position/velocity of atomic clouds.

dG/G ~ 0.3%

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

differential accelerometer
Differential accelerometer

~ 1 m

Applications in precision navigation and geodesy

slide11

Gravity gradiometer

Demonstrated accelerometer resolution: ~10-11 g.

truck based gravity gradient survey 2007
Truck-based gravity gradient survey (2007)

ESIII loading platform survey site

gravity gradient survey
Gravity gradient survey

Gravity anomally map from ESIII facility

Gravity gradient survey of ESIII facility

test newton s inverse square law
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
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.

Also, new tests of General Relativity

10 m atom drop tower

Atomic source

10 m drop tower

post newtonian gravitation

laser

atom

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.

Atom and photon geodesics

Collaborators: Savas Dimopoulos, Peter Graham, Jason Hogan.

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.

parameterized post newtonian ppn analysis
Parameterized Post-Newtonian (PPN) analysis

Schwazchild metric, PPN expansion:

  • 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).

Corresponding AI phase shifts:

Projected experimental limits:

(Dimopoulos, et al., PRL 2007)

error model
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)
gravity wave detection
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
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
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.

terrestrial sensor
Terrestrial Sensor

1 km

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

seismic noise
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
(Possible) DUSEL Installation

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

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

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

(data courtesy of Vuk Mandic, UofM)

cosmology
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

Giulini, gr-qc/0602098

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

Interesting phenomenology from exotic/speculative theories?

future
Future
  • Wavepackets separated by z = 10 m, for T = 1 sec. For Earth gravity field: Df~ mgzT/h ~ 2x1011rad
  • Signal-to-noise for read-out: SNR ~ 105:1 per shot. (squeezed state atom detection, 108 atoms per shot)
  • Resolution to changes in g per shot: dg ~ 1/(Df SNR) ~ 4x10-17 g
  • 106 shots data collection: dg ~ 4x10-20 g (!)

How do we exploit this sensitivity?

towards macroscopic quantum interference
Towards macroscopic quantum interference

Df ~ mgzT/h

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
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.