Download .pdf file

Precision
Atom Interferometry
Prof. Mark Kasevich
Dept. of Physics and Applied Physics
Stanford University, Stanford CA
Outline
Light-pulse de Broglie wave interferometry overview
Existing Sensors
Rotation (Gyroscope)
Gravimetric (Gravity Gradiometer)
Sensors for Science
Testing Newton’s inverse square law
Equivalence principle
Gravity beyond Newton
Gravity wave detection
Testing atomic charge neutrality
Quantum Metrology
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)
(Light-pulse) atom interferometry
Resonant optical
interaction
|2〉
|1〉
2-level atom
Resonant traveling
wave optical
excitation,
(wavelength λ)
Recoil diagram
Momentum conservation between
atom and laser light field (recoil
effects) leads to spatial separation
of atomic wavepackets.
Phase shift calculation methodology
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.
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
Laboratory gyroscope
Gyroscope interference
fringes:
AI gyroscope
Sensor
noise
Noise:
3 µdeg/hr1/2
Bias stability:
< 60 µdeg/hr
Scale factor:
< 5 ppm
Atom shot noise
Gustavson, et al., PRL, 1997,
Durfee, et al., PRL, 2006
Lab technical
noise
Measurement of Newton’s Constant
Use differential atom interferometer
accelerometers (rejects spurious
technical vibrations).
Pb mass translated vertically along
gradient measurement axis.
Yale, 2002 (Fixler PhD thesis)
Characterization of source mass
geometry and atom trajectories
allows for determination of Newton’s
constant G.
Measurement of G
Systematic error sources dominated by initial position/velocity of
atomic clouds. δG/G ~ 0.3%
Fixler PhD thesis, 2003; Fixler, et al., Science, 2007.
Differential accelerometer
~1m
Applications in precision navigation and geodesy
Gravity gradiometer
Demonstrated accelerometer
resolution: ~1x10-11 g.
Gravity gradient survey
Gravity anomally
map from ESIII
facility (top view)
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.
Compact 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
A quantum sensor …. coherence length
Measurement of coherence
length of laser cooled atomic
source (~ 100 nm)
Time-skewed
pulse sequence to
reject spurious
mutli-path
interferences
Interior view of sensor
UHV vacuum
enclosure; Cs
atomic source
Discrete optics for
laser beams,
magnetic field
control;
photodiodes ….
Equivalence Principle
Use atom interferometric
differential accelerometer to test EP
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 g limited by magnetic
field inhomogeneities and gravity
anomalies.
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.
laser
atom
Post-Newtonian trajectories for classical
particle:
• 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.
Parameterized Post-Newtonian (PPN) analysis
Schwazchild metric, PPN expansion:
Steady path of
apparatus
improvements
include:
Corresponding AI phase shifts:
• Improved atom
optics
• 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, PRD 2008)
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.
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 Wave Detection
Metric:
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.
Gravity wave induced phase shift:
h is strain, L is separation, T is pulse
separation time, ω is frequency of
wave
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).
Proposed Terrestrial Detector Performance
1 km
Dimopoulos, Graham, Hogan, Kasevich, Rajendran, 2008 (archive, submitted)
Seismic Noise
Seismic noise induced strain analysis for
LIGO (Thorne and Hughes, PRD 58)
.
Primary disturbances are surface waves.
Suggests location in underground facility.
Seismic fluctuations
give rise to
Newtonian gravity
gradients which can
not be shielded.
Data courtesy of
Vuc Mandic
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.
Atomic Physics Technical Challenges
• Advanced, high flux atom source development
– high rep rate, high flux source of cold atoms
– 10 Hz, 108 atoms/shot
– requires incremental advances in current technology
• Large momentum transfer atom optics
–
–
–
–
Enhances sensitivity
Demonstrated N ~ 10
Desired N ~ 100
Work in progress
Atom charge neutrality
• Apparatus will support >1 m wavepacket separation
• Enables ultra-sensitive search for atom charge neutrality
through scalar Aharonov-Bohm effect.
ε = δe/e ~ 10-26 for mature
experiment using scalar
Aharonov-Bohm effect
Current limit: δe/e ~ 10-20
(Unnikrishnan et al., Metrologia
41, 2004)
Impact of a possible observed
imbalance currently under
investigation.
Phase shift:
Theory collaborators:
A. Arvanitaki, S. Dimopoulos,
A. Geraci, PRL 2008.
Quantum Metrology: Sub-shot noise detection
Atom shot noise limits sensor performance.
Recently evolving ideas in quantum information science have
provided a road-map to exploit exotic quantum states to significantly
enhance sensor performance.
– Sensor noise scales as 1/N where N is the number of particles
– “Heisenberg” limit
– Shot-noise ~ 1/N1/2 limits existing sensors
Challenges:
– Demonstrate basic methods in laboratory
– Begin to address engineering tasks for realistic sensors
Impact of successful implementation for practical position/time
sensors could be substantial. Possible 10x – 100x reduction in
sensor noise.
Enables crucial trades for sensitivity, size and bandwidth.
QND atom detection in high finesse cavity
Dispersive
cavity shift
MOT located in 300 µm waist of
200K finesse (3 kHz linewidth)
optical cavity.
Cavity frequency shift (kHz)
7
6
5
4
3
2
1
0 100 200 300 400 500
Microwave pulse duration (microseconds)
(Poster, Igor Teper; Tuchman, et al. PRA, 2006, Long, Opt. Lett., 2007)
Rabi
oscillations
detected via
cavity shift
State evaluation via QND back-action
Use QND probe to
prepare spin squeezed
state.
Measurement backaction: dispersion in AC
Stark shift due to
photon number
fluctuations associated
with coherent optical
state in cavity.
Observe back-action by
rotation of atomic state
on Bloch sphere using a
microwave pulse.
Measured number
fluctuations (induced by
QND back-action) agree
with theory.
Control
2.5 nW
probe
1.2 nW
probe
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, Graduate student, Applied physics
Jongmin Lee, Graduate student, Electrical engineering
Chetan Mahadeswaraswamy, Graduate student, Mechanical engineering
David Johnson, Graduate student, Aero/Astro engineering
Geert Vrijsen, Graduate student, Applied physics
Jason Hogan, Graduate student, Physics
Sean Roy, Graduate student, Physics
Tim Kovachy, Undergraduate
Paul Bayer, Engineer
+ THEORY COLLABORATORS:
S. Dimopolous, P. Graham, S. Rajendran, A. Arvanitaki, A. Geraci
+ AOSense team
B. Young, T. Gustavson, J. Spilker, A. Black, F. Roller, T. Tran, M. Mathews, A.
Vitushkin, B. Dubetsky.