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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
Slits
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
As atom climbs gravitational potential,
velocity decreases and wavelength
increases
Rotations
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)
A
(Light-pulse) atom interferometry
Resonant optical
interaction
|2
|1
2-level atom
Resonant traveling
wave optical
excitation,
(wavelength l)
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 mdeg/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.
dG/G ~ 0.3%
Fixler, et al., Science, 2007,
also Fixler PhD thesis, 2003.
Differential accelerometer
~1m
Applications in precision navigation and geodesy
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
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
10 m atom drop tower
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
Atomic
source
10 m drop tower
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.
laser
atom
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
Schwazchild metric, PPN expansion:
Steady path of
apparatus
improvements
include:
Corresponding AI phase shifts:
• Improved atom
optics (T.
Kovachy)
• Taller apparatus
• Sub-shot noise
interference readout
Projected experimental limits:
• 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
dg ~ 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
1 km
DUSEL facility: 1 km vertical shaft at Homestake
mine. In the future, deeper shafts may be
available.
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
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
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
1) Wavepackets separated by z = 10 m, for T = 1 sec.
For Earth gravity field: Df ~ mgzT/h ~ 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:
dg ~ 1/(Df SNR) ~ 4x10-17 g
4) 106 shots data collection: dg ~ 4x10-20 g (!)
How do we exploit this sensitivity?
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 >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.