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

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 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 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 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 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 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 laser 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: 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 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 How do we exploit this sensitivity? 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 ~ 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 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.