Jason HoganStanford University

January 17, 2013

Seoul National UniversitySeoul, Korea

Prospects for gravitational wave detection with atom interferometry

Topics

Atom interferometryin a 10 meter tower

Gravitational wavedetection with atoms

Cold Atom Inertial Sensors

AI gyroscope (1997)

Cold atom sensors:• Laser cooling; ~108 atoms, ~uK (no cryogenics)• Atom is freely falling (inertial test mass)• Lasers measures motion of atom relative to sensor case• Accelerometers, gravimeters, gyroscopes, gradiometers

AI compact gyroscope (2008)

Technology evolution:

AOSense commercial AI gravimeter (2011)

Light Pulse Atom Interferometry

• Vertical atomic fountain• Atom is freely falling• Lasers pulses are atom beamsplitters & mirrors• pulse sequence

• Interior view

F=3

F=4

10 m Accelerometer Sensitivity10 m atom drop tower

2T ~ 2.3 sK eff = 2k

Shot noise limited detection @ 107 atoms per shot:

(~ 1 month)

State of the art: “LMT” beamsplitters with

rad

[S Chiow et al., Phys. Rev. Lett. 107, 130403 (2011).]= 102 k

Atom Interferometry~

10 m

2.3 s

t = T: Image at apex

1.5 cm

F=1 F=2

Design Goal: 10-15 g Test of the Equivalence Principle

F=1

F=2(pushed)

1 cm

2T = 2.3 s: Images of Interferometry

≈ 4 mm/s

Apparatus

• Ultracold atom source– >106 at 50 nK

• Optical Lattice Launch– 13.1 m/s with 2372

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

Beam Angle Phase

Position:

Phase imprinted by beam angle (small ):

g

Coriolis Phase

Phase imprinted by beam angle (small ):

Coriolis Effect

Uniform Rotation Rate Coriolis:

Gustavson et al. PRL 78, 1997McGuirk et al. PRA 65, 2001

Hogan et al. Enrico Fermi Proceedings, 2009Lan et al. PRL 108, 2012

Coriolis Phase

Uniform Rotation Rate Coriolis:

Phase imprinted by beam angle (small ):

Coriolis Compensation

Gustavson et al. PRL 78, 1997McGuirk et al. PRA 65, 2001

Hogan et al. Enrico Fermi Proceedings, 2009Lan et al. PRL 108, 2012

Rotation Compensation System

nanopositioner (x3)

mirror

• < 1 nrad measured precision• ~ 1 nrad repeatability• Piezoresistive position sensors • Rigidly anchored to quiet floor

In-vacuum nanopositioning stage & mirror

Anchor plate

Coarse alignment

Single-shot Phase & Contrast

g

1 cm

F = 2(pushed)

F = 1

≈ 4 mm/s

g

1 cmF = 2

(pushed)

F = 1

60 μrad misalignment at final pulse

Single-shot Phase & Contrast

60 μrad misalignment at final pulse

g

1 cm

F = 2(pushed)

F = 1

≈ 4 mm/s

g

1 cmF = 2

(pushed)

F = 1

Single-shot Phase & Contrast

60 μrad misalignment at final pulse

g

1 cm

F = 2(pushed)

F = 1

≈ 4 mm/s

g

1 cmF = 2

(pushed)

F = 1

Single-shot Phase & Contrast

60 μrad misalignment at final pulse

g

1 cm

F = 2(pushed)

F = 1

≈ 4 mm/s

g

1 cmF = 2

(pushed)

F = 1

Spatial Frequency vs Phase Shear

θ (μrad) Spatial Fringes

80

40

0

-40

-80

Beam angle phase:

Fringe spatial frequency:+ correction for drift time to imaging

Coriolis Compensated

Application: Gyrocompassing

Beam Angle + Coriolis Error:

gTrue north:

Precision: 20 mdegRepeatability: ~ 1 mdegCorrection to axis: -0.93 deg

• Large momentum transfer (LMT) beamsplitters – multiple laser interactions• Each laser interaction adds a momentum recoil and imprints the laser’s phase

Example LMT interferometerLMT energy level diagram

Phase amplification factor N

LMT Beamsplitters: Coherent Phase Amplification

High Contrast LMT Atom Interferometers

Coming Next:

LMT atom optics in 10 m tower

~1 m wavepacket separation

7 x 10-14 g / shot

Chiow, PRL (2011)

70% contrast

18% contrast

Topics

Atom interferometryin a 10 meter tower

Gravitational wavedetection with atoms

Gravitational Wave Detection

Why consider atoms?

• Neutral atoms are excellent “test particles” (follow geodesics)

• Atom interferometry provides exquisite measurement of geodesic w.r.t. laser “ruler” (LMT phase amplification)

• Flexible operation modes (broadband, resonant detection)

• Single baseline configuration possible (e.g., only two satellites)

Gravitational Wave Phase Shift Signal

Relativistic Calculation:

Laser ranging an atom (or mirror) that is a distance L away:

Position

Acceleration

Phase Shift:

Vibrations and Seismic Noise

• Atom test mass is inertially decoupled (freely falling); insensitive to vibration

• Atoms analogous to LIGOs mirrors

• However, the lasers vibrate

• Laser has phase noise

Laser vibration and intrinsic phase noise are transferred to the atom’s phase via the light pulses.

Differential Measurement

0

Differential Measurement

Light from the second laser is not exactly common

Light travel time delay is a source of noise

Single photon transitions avoid this problem

Terrestrial Configuration• Run two, widely separated interferometers using

common lasers• Measure the differential phase shift

(e.g., vertical mine shaft)

Benefits:1. Signal scales with length L ~ 1 km

between interferometers (easily increased)2. Common-mode rejection of seismic &

phase noise

Allows for a free fall time T ~ 1 s. (Maximally sensitive in the ~1 Hz band)

Gravity Gradient Noise Limit

Seismic fluctuations give rise to Newtonian gravity gradients which can not be shielded.

Seismic noise induced strain analysis for LIGO (Thorne and Hughes, PRD 58).

Allows for terrestrial gravitational wave detection down to

~ 0.3 Hz

Projected Terrestrial GW Sensitivity

Satellite ConfigurationCommon interferometer laser

10 – 50 m

L ~ 1000 km

10 – 50 m

Strain Sensitivity

L=106 m baseline100 ħk10-4 rad/Hz1/2

T =100 s60 m booms

• Space-based atom GW detector could have science potential comparable to LISA• Flexible atom optics allows for both “broadband” and “resonant” modes

RequirementsAnalysis to determine requirements on satellite jitter, laser pointing stability, atomic source stability, and orbit gravity gradients.

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

Laser frequency noise insensitive detectorAll previous interferometric GW detectors need multiple baselines or ultra stable lasers.

arXiv:1206.0818

• Long-lived single photon transitions (e.g. clock transition in Sr, Ca, Yb, etc.)• Atoms act as clocks, measuring the light travel time across the baseline (time in excited state).• GWs modulate the laser ranging distance.

Laser noise is common

Excitedstate

LMT with single photon transitions

Example LMT beamsplitter (N = 3)

• Interesting sensitivity requires Large Momentum Transfer (LMT) atom optics (large N).

• LMT realized by sequential pulses from alternating directions.• Selectively accelerate one arm with a series of pulses

Reduced Noise SensitivityIntrinsic laser noise cancels. What are the remaining sources of noise?

Differential phase shifts (kinematic noise) suppressed by Dv/c < 3×10-11

Any relative velocity Δv between the interferometers affects the time spent in the excited state, leading to a differential phase shift.

1. Platform acceleration noise da2. Pulse timing jitter dT3. Finite duration Dt of laser pulses4. Laser frequency jitter dk

Leading order kinematic noise sources:

Some Differences

• Atom plays the role of proof mass and phase meter• Phase amplification (LMT, resonant detection protocols)• Shorter baseline at LISA sensitivity (e.g., 1000 km)• Atom proof mass is disposable, properties universal• Neutral atom insensitive to EM disturbances• Intrinsic laser phase noise insensitivity• Single baseline configurations without ultra stable lasers

(two satellites instead of three)• Reduced kinematic noise requirements (drag free control,

GRS)

CollaboratorsNASA Goddard Space Flight Center

Babak SaifBernard D. SeeryLee FeinbergRitva Keski-Kuha

Stanford UniversityPI:

Mark KasevichEP:

Susannah DickersonAlex Sugarbaker

LMT:Sheng-wey ChiowTim Kovachy

Theory:Peter GrahamSavas DimopoulosSurjeet Rajendran

Former members:David Johnson (Draper)Jan Rudolf (Rasel Group)

Also:Philippe Bouyer (CNRS)