experimental tests of the weak equivalence principle susannah dickerson, kasevich group, stanford...
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Experimental testsof the weak equivalence principle
Susannah Dickerson, Kasevich Group, Stanford University2nd 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
![Page 6: Experimental tests of the weak equivalence principle Susannah Dickerson, Kasevich Group, Stanford University 2 nd International Workshop on Antimatter](https://reader035.vdocument.in/reader035/viewer/2022062422/56649e8a5503460f94b8ff9e/html5/thumbnails/6.jpg)
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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Historical trend
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 force vector 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)
(ano
mal
ous
frac
tiona
l acc
eler
ation
)
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)Experiment Precision Material
Atom interferometry
Stanford 10-15 85Rb-87Rb
Berkeley 10-14 6Li-7Li
Hannover (QUANTUS-II) 10-11 40K-87Rb
Paris (ICE) 10-11 39K-87Rb; parabolic flight
Macroscopic proof masses
Torsion Balance (Eot-Wash) 10-14 Be-Polyethylene
LLR 10-14 Earth-moon
Galileo Galilei on Ground 10-16 Rapidly-rotating concentric masses
SR-POEM 10-17 Sounding rocket;
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Space-based tests (matter only)Experiment Precision Material
Atom interferometry
STE-QUEST 10-15 85Rb-87Rb
Macroscopic proof masses
MICROSCOPE 10-15 (rotating) concentric masses, Pt-T
STEP 10-18 Rotating concentric masses; Be, Nb, Pt-Ir
Galileo Galilei 10-17 Rapidly-rotating concentric masses
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Direct antimatter testsExperiment Precision Material
Already performed
ALPHA 102 Free fall of Ħ
Operating/planned
AEGIS 10-2 Moiré deflectometry of Ħ
ALPHA 10-2 Atom interferometry of Ħ
GBAR 10-2 Free fall of Ħ
AGE 10-2 Grating atom interferometry of Ħ
Semi-direct (already performed)
CP LEAR 10-9 K0 – anti-K0 oscillations
ATRAP 10-4 p – anti-p cyclotron frequencies
Supernova 1987A 10-2-10-6 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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Atom Interferometry
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Atom Interferometry
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
– 107 at 50 nK– 105 at 3 nK
• Optical Lattice Launch– 13.1 m/s with 2386 photon
recoils to 9 m
• Atom Interferometry– 2 cm 1/e2 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, 105 atoms 50 nK, 4 x 106 atoms
F=2(pushed)
F=1
Dickerson, et al., PRL 111 (2013)
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Dickerson, et al., PRL 111 (2013)
Atom Interferometry
3 nK, 105 atoms 50 nK, 4 x 106 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, 1997McGuirk et al. PRA 65, 2001
Hogan et al. Enrico Fermi Proceedings, 2009Lan 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 ShearsInterferometer output atom population:
Contrast Interferometer phase
Sugarbaker, et al., PRL 111 (2013)
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Phase ShearsInterferometer 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:
CCD
2
CCD1
y
xz
CCD1:
CCD2:
Mirror
Rotation vector
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Dual-Axis Gyroscope
Rotation phase shift:
CCD
2
CCD1
y
xz
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 tower2T = 2.3 seconds
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Collaborators
Stanford University: PI:
Mark KasevichEP:
Jason HoganSusannah DickersonAlex SugarbakerTim Kovachy
Former members:Sheng-wey ChiowDave JohnsonJan Rudolph (Rasel Group)
Also:Philippe Bouyer (CNRS)
Supported by:SD: Gerald J. Lieberman Fellowship AS: National Science Foundation GRF TK: Hertz Foundation