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Atom Interferometry
Prof. Mark Kasevich
Dept. of Physics and Applied Physics
Stanford University, Stanford CA
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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)
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Simple models for inertial force sensitivity
Gravity/Accelerations
g
(longer de Broglie wavelength)
As atom climbs gravitational potential, velocity decreases and wavelength increases
A
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)
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Resonant traveling wave optical excitation, (wavelength )
(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.
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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 source:www.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: < 100 deg/hr1/2
• 10 deg/s max input• <100 ppm absolute accuracy
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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.
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Measurement of G
Systematic error sources dominated by initial position/velocity of atomic clouds.G/G ~ 0.3%
Fixler, et al., Science, 2007, also Fixler PhD thesis, 2003.
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Differential accelerometer
Applications in precision navigation and geodesy
~ 1 m
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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 Newton’s Inverse Square Law
Using new sensors, we anticipate G/G ~ 10-5.
This will also test for deviations from the inverse square law at distances from ~ 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 < 1 K to enforce tight control over kinematic degrees of freedom
Statistical sensitivity
g ~ 10-15 g with 1 month data collection
Systematic uncertainty
g ~ 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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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
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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)
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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 g ~ 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 > 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 exp’t
White dwarft
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Terrestrial Sensor
DUSEL facility: 1 km vertical shaft at Homestake mine. In the future, deeper shafts may be available.
1 km
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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
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)
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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(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
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Future
1) Wavepackets separated by z = 10 m, for T = 1 sec. For Earth gravity field: ~ 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: g ~ 1/( SNR) ~ 4x10-17 g
4) 106 shots data collection: g ~ 4x10-20 g (!)
How do we exploit this sensitivity?
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Towards macroscopic quantum interference
~ 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. NanostructuresQND correlated many-body states
Weakly bound quasi-particles
Possible interference with >106 amu objects. Entanglement via gravitational interaction?
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Fundamental limits?
Are there fundamental limits?
Penrose collapseNon-linearity in quantum mechanicsSpace-time fluctuations (eg. due to
Planck–scale fluctuations)
In coming years, AI methods will provide a >106-fold improvement in sensitivity to such physics.