PROBING the MYSTERY: THEORY & EXPERIMENT in QUANTUM GRAVITY Tests of gravity and the quantum superposition principle using atom interferometry PROBING the MYSTERY: THEORY & EXPERIMENT in QUANTUM GRAVITY Galiano Island Jason Hogan Stanford University August 19, 2015

Quantum superposition at the meter scale 54 cm Image of the wavepackets in an LMT interferometer with record 54 cm wavepacket separation. Visualization of the wavefunction

Atom interference Light interferometer Atom interferometer Light fringes Atom interferometer Beamsplitter Atom fringes Atom Beamsplitter Mirror http://scienceblogs.com/principles/2013/10/22/quantum-erasure/ http://www.cobolt.se/interferometry.html

Light Pulse Atom Interferometry Long duration Large wavepacket separation

10 meter scale atomic fountain < 3 nK

Interference at long interrogation time Port 1 Port 2 Wavepacket separation at apex (this data 50 nK) 2T = 2.3 sec; Near full contrast 6.7×10-12 g/shot (inferred) Demonstrated statistical resolution: ~5 ×10-13 g in 1 hr (87Rb) Interference (3 nK cloud) Dickerson, et al., PRL 111, 083001 (2013).

Phase shear readout Phase Shear Readout (PSR) F = 2 (pushed) F = 1 g 1 cm 1 cm ≈ 4 mm/s Single-shot interferometer phase measurement Purposefully misalign interferometer (tilt last pulse) Introduces phase shear: fringes Differential phase across cloud is stable

Phase shear readout Phase Shear Readout (PSR) F = 2 (pushed) F = 1 g 1 cm 1 cm ≈ 4 mm/s Single-shot interferometer phase measurement Purposefully misalign interferometer (tilt last pulse) Introduces phase shear: fringes Differential phase across cloud is stable

Phase shear readout Phase Shear Readout (PSR) F = 2 (pushed) F = 1 g 1 cm 1 cm ≈ 4 mm/s Single-shot interferometer phase measurement Purposefully misalign interferometer (tilt last pulse) Introduces phase shear: fringes Differential phase across cloud is stable

Phase shear readout Phase Shear Readout (PSR) F = 2 (pushed) F = 1 g 1 cm 1 cm ≈ 4 mm/s Single-shot interferometer phase measurement Purposefully misalign interferometer (tilt last pulse) Introduces phase shear: fringes Differential phase across cloud is stable

LMT sequence details Sequential π-pulses (2ħk) applied to one arm after initial beamsplitter Bragg atom optics (fixed internal state) Gaussian π-pulses 60 µs FWHM 30 GHz detuning

Wavepacket separation 54 cm Stitched image (36 images)

Wavepacket separation . . . 54 cm Stitched image (36 images)

Wavepacket separation . . . 90 ħk . . . 54 cm Stitched image (36 images)

Interferometer ports 2 ħk 90 ħk Interference causes population modulation between the ports

Phase shear from time asymmetry Delay last pulse + δT Phase from Doppler shift Vertical shear due to asymmetric pulse spacing: 2 ħk data -240 µs -160 µs 0 µs 160 µs 240 µs Müntinga et al., PRL 2013 Sugarbaker, et al., PRL 2013

Contrast Envelope Fringes from time asymmetry will reduce contrast if not resolved Measured contrast envelopes: Interferometer time asymmetry Modulation depth 30 ħk 60 ħk 90 ħk Equivalently: 8*10^9 rad/g for 90 hk Coherence length (Manuscript submitted)

Contrast vs LMT order High contrast out to 90 ħk Photon recoils (ħk) 54 cm High contrast out to 90 ħk All data using 2T = 2.08 s Amplitude fluctuations not caused by interference 8*10^9 rad/g for 90 hk (Manuscript submitted)

Spatial interference fringes Time asymmetry: “Cosine” “Sine” 30 ħk Port 1 Fitted wavelength agrees with theory Port 2 Principal component analysis Complementary way to observer contrast. Fringe wavelength is determined by dT and n, matches theory. H. Müntinga et al., Phys. Rev. Lett. 110, 093602 (2013). S. Dickerson et al., Phys. Rev. Lett. 111, 083001 (2013).

Comparison of matter wave interferometers Cesium 2012: S.Y. Lan et. al., PRL 108, 090402 (2012). PFNS8 Molecules 2011:  S. Gerlich et. al., Nature Communications 2, 263 (2011). Cesium 2009:  K. Y. Chung et. al., PRD 80, 016002 (2009). C70 Molecules 2002:  B. Brezger et. al., PRL 88, 100404 (2002). Neutrons 2001:  M. Zawisky et. al., Nuc. Instr. and Meth. in Phys. Research A 481, 406-413 (2002). Cesium 2001:  A. Peters, K. Y. Chung, and S. Chu, Metrologia 38, 25 (2001). Sodium 1992:  M. Kasevich and S. Chu, Appl. Phys. B 54, 3210332 (1992).

Bounds for modifications of quantum mechanics Nimmrichter and Hornberger (PRL 2013) “Macroscopicity” “Minimal modification of quantum mechanics … to classicalize” Predicts decay of quantum superposition above some critical length scale, time. Cesium 2012: S.Y. Lan et. al., PRL 108, 090402 (2012). PFNS8 Molecules 2011:  S. Gerlich et. al., Nature Communications 2, 263 (2011). Cesium 2009:  K. Y. Chung et. al., PRD 80, 016002 (2009). C_70 Molecules 2002:  B. Brezger et. al., PRL 88, 100404 (2002). Neutrons 2001:  M. Zawisky et. al., Nuclear Instruments and Methods in Physics Research A 481, 406-413 (2002). Cesium 2001:  A. Peters, K. Y. Chung, and S. Chu, Metrologia 38, 25 (2001). Sodium 1992:  M. Kasevich and S. Chu, Appl. Phys. B 54, 3210332 (1992).

General relativistic phase shifts Light-pulse interferometer phase shifts in GR: 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 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.

General Relativity Effects Schwarzschild metric, PPN expansion: Newtonian Gravity Gravity Gravitates Kinetic Energy Gravitates Corresponding AI phase shifts: Projected experimental limits: (Dimopoulos, et al., PRL 2007; PRD 2008)

Gravitational Wave Detection Why study gravitational waves? New carrier for astronomy Extreme tests of gravity Early universe cosmology Why consider atoms? Neutral atoms are excellent proof masses Atom interferometry to measure geodesic Atoms are excellent clocks

Satellite GW Antenna Common interferometer laser 100 km – 1000 km Atoms Atoms 100 km – 1000 km JMAPS bus/ESPA deployed

Single photon atom interferometry Single photon gradiometer Example LMT beamsplitter (N = 3) AI with single photon transitions: Laser noise suppression using a single baseline LMT using pulses from alternating directions Candidate transition

Potential Strain Sensitivity J. Hogan, et al., GRG 43, 7 (2011).

Heterodyne laser link for long baselines Measure heterodyne beat between incoming reference laser and local oscillator laser. LO is phase locked to reference, so laser noise is still common between the two AIs. Insensitive to motion of beam splitter LO has high intensity for driving transitions M1, M1: Master lasers LO1, LO2: Local oscillator lasers R1, R2: Reference beams BS: Beam splitter TTM: Tip-tilt mirror J. Hogan and M. Kasevich, arXiv:1501.06797 (2015)

Long baseline strain sensitivity Averaged over GW direction and polarization Sr atoms LISA-like sensitivity with conservative 2ħk design 10x better than LISA with LMT New tool for optimizing detector design J. Hogan and M. Kasevich, arXiv:1501.06797 (2015)

Collaborators Stanford NASA GSFC AOSense Support: Mark Kasevich Tim Kovachy Christine Donnelly Chris Overstreet Peter Asenbaum Theory: Peter Graham Savas Dimopoulos Surjeet Rajendran Former members: Susannah Dickerson Alex Sugarbaker David Johnson Sheng-wey Chiow Visitors: Philippe Bouyer (CNRS) Jan Rudolph (Hannover) NASA GSFC Babak Saif Bernard D. Seery Lee Feinberg Ritva Keski-Kuha AOSense Brent Young (CEO) Support:

Example Interference Data

AC Stark shift compensation Intensity ripples change with height (diffraction): 30 ħk Fractional contrast AC Stark shift difference for large wavepacket separation Height (Rabi frequency fixed) Atom optics laser Effective sideband asymmetry Atom optics Absolute Stark shift compensation F=2 F=1