1. Experimental tests of the weak equivalence principle Susannah Dickerson, Kasevich Group, Stanford University 2 nd International Workshop on Antimatter and Gravity November 13, 2013

2. The Weak Equivalence Principle Independent of mass or composition, all bodies locally fall under gravity at the same rate rate.

3. The Weak Equivalence Principle Independent of mass or composition, all bodies locally fall under gravity at the same rate rate.

4. 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

5. 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

6. 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

7. Historical trend

8. LLR = Lunar Laser Ranging

9. 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

10. 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)

11. 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)

12. 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;

13. 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

14. 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

15. Towards testing the WEP with atom interferometry

16. Atom Interferometry

18. Influences on phase shift: Acceleration Rotation Gravity gradients Magnetic fields

19. Atom Interferometry Influences on phase shift: Acceleration Rotation Gravity gradients Magnetic fields ~ 10 m 2.3 s

20. 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)

21. 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

22. 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

23. Atom Interferometry 3 nK, 10 5 atoms50 nK, 4 x 10 6 atoms F=2 (pushed) F=1 Dickerson, et al., PRL 111 (2013)

24. Atom Interferometry 3 nK, 10 5 atoms50 nK, 4 x 10 6 atoms F=2 (pushed) F=1 Acceleration sensitivity:

25. Precision measurement of Earth’s rotation

26. 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

27. Point Source Interferometry – Long time of flight x-p correlation – Velocity-dependent phase phase gradient Phase:Ballistic expansion Dickerson, et al., PRL 111 (2013)

28. Phase Shears Interferometer output atom population: Contrast Interferometer phase Sugarbaker, et al., PRL 111 (2013)

29. 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)

30. 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)

31. Dual-Axis Gyroscope Rotation phase shift: CCD2 CCD1 y x z CCD1: CCD2: Mirror Rotation vector

32. Dual-Axis Gyroscope Rotation phase shift: CCD2 CCD1 y x z CCD1: CCD2: CCD1 CCD2 Precision: Noise Floor: Mirror

33. Gyrocompassing Beam Angle + Coriolis Error: g True north: Precision: Repeatability: Correction to axis: Sugarbaker, et al., PRL 111 (2013)

34. Large-momentum transfer (Current line of research)

35. Near-term goal: with … wavepacket separation, in a shot LMT Atom Interferometry Sensitivity increase: 102ħk demonstration: Chiow et al. PRL 107, 2011

36. Wavepacket separation at the top: 4 cm LMT with long interrogation time 6 ħk sequential Raman in 10 meter tower 2T = 2.3 seconds

37. 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