Atom Interferometry

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Atom Interferometry

• Prof. Mark Kasevich
• Dept. of Physics and Applied Physics
• Stanford University, Stanford CA

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Youngs double slit with atoms
Youngs 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
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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 105
rad (Previous experiments with neutrons)
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(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)
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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 sourcewww.nobel.se/physics
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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.
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Gyroscope
Measured gyroscope output vs.orientation
Typical interference fringe record

• Inferred ARW lt 100 mdeg/hr1/2
• 10 deg/s max input
• lt100 ppm absolute accuracy

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Measurement of Newtons 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 Newtons constant G. Use
gravity gradiometer to reject spurious technical
vibrations.
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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.
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Differential accelerometer
1 m
Applications in precision navigation and geodesy
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Gravity gradiometer
Demonstrated accelerometer resolution 10-11 g.
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Truck-based gravity gradient survey (2007)
ESIII loading platform survey site
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Gravity gradient survey
Gravity anomally map from ESIII facility
Gravity gradient survey of ESIII facility
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Test Newtons 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.
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Equivalence Principle
Co-falling 85Rb and 87Rb ensembles Evaporatively
cool to lt 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
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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.
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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 reqd).

Corresponding AI phase shifts
Projected experimental limits
(Dimopoulos, et al., PRL 2007)
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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)

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Equivalence Principle Installation
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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
gt 40 Hz.
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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)
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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.
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Stochastic Sources/Satellite expt
White dwarft
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Terrestrial Sensor
1 km
DUSEL facility 1 km vertical shaft at Homestake
mine. In the future, deeper shafts may be
available.
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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.
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(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)
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Cosmology

• Are there (local) observable phase shifts of
  cosmological origin?
• Analysis has been limited to simple metrics
• FRW ds2 dt2 a(t)2(dx2dy2dz2)
• McVittie Schwarzchild FRW

Giulini, gr-qc/0602098
No detectable local signatures for Hubble
expansion (shift H2) Interesting phenomenology
from exotic/speculative theories?
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Future

• Wavepackets separated by z 10 m, for T 1 sec.
  For Earth gravity field Df
  mgzT/h 2x1011 rad
• Signal-to-noise for read-out SNR 1051 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?

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Towards macroscopic quantum interference
Gravitational phase shift scales linearly with
mass of interfering particle (quasi-particle).

• Df mgzT/h

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 gt106
amu objects. Entanglement via gravitational
interaction?
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Fundamental limits?
Are there fundamental limits? Penrose
collapse Non-linearity in quantum
mechanics Space-time fluctuations (eg. due to
Planckscale fluctuations) In coming years, AI
methods will provide a gt106-fold improvement in
sensitivity to such physics.