Experimental tests of the weak equivalence principle Susannah Dickerson, Kasevich Group, Stanford...

Experimental testsof the weak equivalence principle

Susannah Dickerson, Kasevich Group, Stanford University2nd International Workshop on Antimatter and Gravity

November 13, 2013

The Weak Equivalence Principle

Independent of mass or composition, all bodies locally fall under gravity at the same rate rate.

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

Historical trend

Historical trend

LLR = Lunar Laser Ranging

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

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)

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)

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;

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

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

Towards testing the WEP with atom

interferometry

Atom Interferometry

Atom Interferometry

Influences on phase shift:• Acceleration• Rotation• Gravity gradients• Magnetic fields

Atom Interferometry

Influences on phase shift:• Acceleration• Rotation• Gravity gradients• Magnetic fields

~ 10

m

2.3 s

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)

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

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

Atom Interferometry

3 nK, 105 atoms 50 nK, 4 x 106 atoms

F=2(pushed)

F=1

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:

Precision measurement of

Earth’s rotation

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

Point Source Interferometry– Long time of flight x-p correlation– Velocity-dependent phase phase gradient

Phase:Ballistic expansion


Phase ShearsInterferometer output atom population:

Contrast Interferometer phase

Sugarbaker, et al., PRL 111 (2013)

Phase ShearsInterferometer output atom population:

No gradient Small gradient(displacement)

Large gradient(fringes)

F = 2(pushed)

F = 1


Phase Shears

No gradient Small gradient(displacement)

Large gradient(fringes)

Interferometer output atom population:

F = 2(pushed)

F = 1


Dual-Axis Gyroscope

Rotation phase shift:

CCD

2

CCD1

y

xz

CCD1:

CCD2:

Mirror

Rotation vector

Dual-Axis Gyroscope

Rotation phase shift:

CCD

2

CCD1

y

xz

CCD1:

CCD2:

CCD1

CCD2

Precision:Noise Floor:

Mirror

Gyrocompassing

Beam Angle + Coriolis Error:

g True north:

Precision:Repeatability:Correction to axis:


Large-momentum transfer(Current line of research)

Near-term goal: with …wavepacket separation, in a shot

LMT Atom Interferometry

Sensitivity increase:

102ħk demonstration: Chiow et al. PRL 107, 2011

Wavepacket separation at the top:

4 cm

LMT with long interrogation time

6 ħk sequential Raman in 10 meter tower2T = 2.3 seconds

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

Experimental tests of the weak equivalence principle Susannah Dickerson, Kasevich Group, Stanford...

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