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Experimental tests of the weak equivalence principle Susannah Dickerson, Kasevich Group, Stanford University 2 nd International Workshop on Antimatter and Gravity November 13, 2013
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The Weak Equivalence Principle Independent of mass or composition, all bodies locally fall under gravity at the same rate rate.
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The Weak Equivalence Principle Independent of mass or composition, all bodies locally fall under gravity at the same rate rate.
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Testing WEP for antimatter Direct measurements – Matter v. antimatter particles under gravity Semi-direct measurements – Matter v. antimatter particles, indirectly under gravity Indirect measurements via matter – Couplings to gravitoscalar/vector force – Contributions of antimatter to mass energy of conventional matter
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Testing WEP for antimatter Direct measurements – Matter v. antimatter particles under gravity Semi-direct measurements – Matter v. antimatter particles, indirectly under gravity Indirect measurements via matter – Couplings to gravitoscalar/vector force – Contributions of antimatter to mass energy of conventional matter
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Testing WEP for antimatter Direct measurements – Matter v. antimatter particles under gravity Semi-direct measurements – Matter v. antimatter particles, indirectly under gravity Indirect measurements via matter – Couplings to gravitoscalar/vector force – Contributions of antimatter to mass energy of conventional matter
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Historical trend
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LLR = Lunar Laser Ranging
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Current Limits of the WEP Lunar Laser Ranging: Torsion Balance: Earth-Moon v. Sun Williams et al, Class. Quant. Grav. 29, 2012 Wagner et al, Class. Quant. Grav. 29, 2012 Be-Ti v. Earth Be-Al v. Earth
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Bounds on antimatter EP from matter Alves et al, arXiv:0907.4110 (2009) Based on LLR, Torsion Balance, and pulsar timing results: (virtual antimatter) (extra forces) Based on Eot-Wash Torsion Balance results: Fifth forcevector force coupled to B – L # ~ 10 -9 -10 -11 Wagner et al. Class. Quantum Grav. 29 (2012)
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Isotopic sensitivity to antimatter EP Hohensee, PRL 111, 2013 (anomalous fractional acceleration) Bounds on antimatter EP violation: 10 -6 – 10 -8 (based on torsion balance, clock comparison and matter waves)
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Ground-based tests (matter only) ExperimentPrecisionMaterial Atom interferometry Stanford10 -1585 Rb- 87 Rb Berkeley10 -146 Li- 7 Li Hannover (QUANTUS-II)10 -1140 K- 87 Rb Paris (ICE)10 -1139 K- 87 Rb; parabolic flight Macroscopic proof masses Torsion Balance (Eot-Wash)10 -14 Be-Polyethylene LLR10 -14 Earth-moon Galileo Galilei on Ground10 -16 Rapidly-rotating concentric masses SR-POEM10 -17 Sounding rocket;
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Space-based tests (matter only) ExperimentPrecisionMaterial Atom interferometry STE-QUEST10 -1585 Rb- 87 Rb Macroscopic proof masses MICROSCOPE10 -15 (rotating) concentric masses, Pt-T STEP10 -18 Rotating concentric masses; Be, Nb, Pt-Ir Galileo Galilei10 -17 Rapidly-rotating concentric masses
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Direct antimatter tests ExperimentPrecisionMaterial Already performed ALPHA10 2 Free fall of Ħ Operating/planned AEGIS10 -2 Moiré deflectometry of Ħ ALPHA10 -2 Atom interferometry of Ħ GBAR10 -2 Free fall of Ħ AGE10 -2 Grating atom interferometry of Ħ Semi-direct (already performed) CP LEAR10 -9 K 0 – anti-K 0 oscillations ATRAP10 -4 p – anti-p cyclotron frequencies Supernova 1987A10 -2 -10 -6 ν – anti-ν arrival times
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Towards testing the WEP with atom interferometry
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Atom Interferometry
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Influences on phase shift: Acceleration Rotation Gravity gradients Magnetic fields
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Atom Interferometry Influences on phase shift: Acceleration Rotation Gravity gradients Magnetic fields ~ 10 m 2.3 s
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Atom Interferometry Sensitivity to phase shift: ~ 10 m 2.3 s Precision Measurements of… Equivalence Principle Gravity curvature/tidal term General Relativity Gravitational waves (future) Antimatter? Hogan et al. Proceedings of Enrico Fermi (2009) Dimopoulos et al. PRL 98, 111102 (2007)
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Apparatus Ultracold atom source – 10 7 at 50 nK – 10 5 at 3 nK Optical Lattice Launch – 13.1 m/s with 2386 photon recoils to 9 m Atom Interferometry – 2 cm 1/e 2 radial waist – 500 mW total power – Dyanmic nrad control of laser angle with precision piezo-actuated stage Detection – Spatially-resolved fluorescence imaging – Two CCD cameras on perpendicular lines of sight
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Atom Interferometry ~ 10 m 2.3 s t = T: Image at apex 1.5 cm F=1 F=2 F=1 F=2 (pushed) 1 cm t = 2T = 2.3s: Images of Interferometry
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Atom Interferometry 3 nK, 10 5 atoms50 nK, 4 x 10 6 atoms F=2 (pushed) F=1 Dickerson, et al., PRL 111 (2013)
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Atom Interferometry 3 nK, 10 5 atoms50 nK, 4 x 10 6 atoms F=2 (pushed) F=1 Acceleration sensitivity:
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Precision measurement of Earth’s rotation
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Coriolis Effect Gustavson et al. PRL 78, 1997 McGuirk et al. PRA 65, 2001 Hogan et al. Enrico Fermi Proceedings, 2009 Lan et al. PRL 108, 2012 Coriolis acceleration: Atom phase: Uncompensated Compensated
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Point Source Interferometry – Long time of flight x-p correlation – Velocity-dependent phase phase gradient Phase:Ballistic expansion Dickerson, et al., PRL 111 (2013)
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Phase Shears Interferometer output atom population: Contrast Interferometer phase Sugarbaker, et al., PRL 111 (2013)
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Phase Shears Interferometer output atom population: No gradient Small gradient (displacement) Large gradient (fringes) F = 2 (pushed) F = 1 Sugarbaker, et al., PRL 111 (2013)
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Phase Shears No gradient Small gradient (displacement) Large gradient (fringes) Interferometer output atom population: F = 2 (pushed) F = 1 Sugarbaker, et al., PRL 111 (2013)
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Dual-Axis Gyroscope Rotation phase shift: CCD2 CCD1 y x z CCD1: CCD2: Mirror Rotation vector
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Dual-Axis Gyroscope Rotation phase shift: CCD2 CCD1 y x z CCD1: CCD2: CCD1 CCD2 Precision: Noise Floor: Mirror
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Gyrocompassing Beam Angle + Coriolis Error: g True north: Precision: Repeatability: Correction to axis: Sugarbaker, et al., PRL 111 (2013)
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Large-momentum transfer (Current line of research)
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Near-term goal: with … wavepacket separation, in a shot LMT Atom Interferometry Sensitivity increase: 102ħk demonstration: Chiow et al. PRL 107, 2011
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Wavepacket separation at the top: 4 cm LMT with long interrogation time 6 ħk sequential Raman in 10 meter tower 2T = 2.3 seconds
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Collaborators Stanford University: PI: Mark Kasevich EP: Jason Hogan Susannah Dickerson Alex Sugarbaker Tim Kovachy Former members: Sheng-wey Chiow Dave Johnson Jan Rudolph (Rasel Group) Also: Philippe Bouyer (CNRS) Supported by: SD: Gerald J. Lieberman Fellowship AS:National Science Foundation GRF TK: Hertz Foundation
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