1. 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

2. 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

3. Atom interference Light interferometer Atom interferometer
Light fringes
Atom interferometer
Beamsplitter
Atom fringes
Atom
Beamsplitter
Mirror

4. Light Pulse Atom Interferometry
Long duration
Large wavepacket separation

5. 10 meter scale atomic fountain
< 3 nK

6. 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, (2013).

7. 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

8. 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

9. 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

10. 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

11. 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

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

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

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

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

16. 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

17. 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)

18. 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)

19. 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, (2013).
S. Dickerson et al., Phys. Rev. Lett. 111, (2013).

20. Comparison of matter wave interferometers
Cesium 2012: S.Y. Lan et. al., PRL 108, (2012). PFNS8 Molecules 2011:  S. Gerlich et. al., Nature Communications 2, 263 (2011). Cesium 2009:  K. Y. Chung et. al., PRD 80, (2009). C70 Molecules 2002:  B. Brezger et. al., PRL 88, (2002). Neutrons 2001:  M. Zawisky et. al., Nuc. Instr. and Meth. in Phys. Research A 481, (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, (1992).

21. 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, (2012). PFNS8 Molecules 2011:  S. Gerlich et. al., Nature Communications 2, 263 (2011). Cesium 2009:  K. Y. Chung et. al., PRD 80, (2009). C_70 Molecules 2002:  B. Brezger et. al., PRL 88, (2002). Neutrons 2001:  M. Zawisky et. al., Nuclear Instruments and Methods in Physics Research A 481, (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, (1992).

22. 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.

23. 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)

24. 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

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

26. 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

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

28. 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: (2015)

29. 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: (2015)

30. 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:

31. Example Interference Data

32. 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