Lecture #2

Gravity Gradiometry and Gravitational Wave Detection

Prof. Mark KasevichDept. of Physics and Applied PhysicsStanford University, Stanford CA

Atom-based Gravitational Wave Detection

Why consider atoms?

• Neutral atoms are excellent proof masses - atom interferometry • Atoms are excellent clocks- optical frequency metrology

Combination of these attributes enables single baseline (2-station) detection of gravitational waves.

atom

laser

General Relativity/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.

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.

Atom and photon geodesics

Tests of General RelativitySchwarzschild metric, PPN expansion:

Corresponding AI phase shifts:

Projected experimental limits:

Steady path of apparatus improvements include:

• Improved atom optics

• Longer baseline• Sub-shot noise

interference read-out

(Dimopoulos, et al., PRL 2007; PRD 2008)

Gravitational waves

Atoms provide inertially decoupled references

Gravity wave phase shift through propagation of optical fields

Evades quantum measurement noise (photon scattering regularized by non-linear atom/photon interaction; prepare fresh atom ensemble each shot)Previous work: B. Lamine, et al., Eur. Phys. J. D 20, (2002); R. Chiao, et al., J. Mod. Opt. 51, (2004); S. Foffa, et al., Phys. Rev. D 73, (2006); A. Roura, et al., Phys. Rev. D 73, (2006); P. Delva, Phys. Lett. A 357 (2006); G. Tino, et al., Class. Quant. Grav. 24 (2007).

Possible satellite configuration

Metric (tt):

Satellite GW Antenna

Common interferometer laser

L ~ 100 - 1000 km

Atoms Atoms

JMAPS bus/ESPA deployed

Atomic physics package

Potential Strain Sensitivity

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

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

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

Analysis details

Curved wavefronts: momentum recoil depends on position in beam.

Design pulse sequences to accommodate Coriolis deflections of wavepacket trajectories and laser wavefront curvature.

5-pulse football sequence

Orbit selection (LEO/MEO/GEO/L2)Challenges

• Determine AI phase shifts for orbiting atoms and lasers, including laser wavefront curvature and inhomogeneities.

• Find configurations which minimize spurious noise sources associated with e.g. satellite attitude control.

• Find configurations which minimize cost.

Wavefront distortion: temporal variations

Time varying wavefront inhomogeneities will lead to non-common phase shifts between distant clouds of atoms

- High spatial frequencies diffract out of the laser beam as the beam propagates between atom clouds

- Limit for temporal stability of wavefronts determined by stability of final telescope mirror

Mirror: Be at 300K

See also, P. Bender, PRD (2011) and Hogan, PRD (2011).

J. M. Hogan, et al., arXiv 1009.2702 (2010), GRG (2011).

Atom cloud kinematic constraints

Shot-to-shot jitter in the position of the atom cloud with respect to the satellite/laser beams constrains static wavefront curvature

Wavefront error vs. spatial frequency, assuming 10 nm/Hz1/2 position jitter

J. M. Hogan, et al., arXiv, 1009.2702 (2010), GRG (2011).

Differential accelerometer

Applications in precision navigation and geodesy

~ 1 m

Gravity gradiometer

Demonstrated accelerometer resolution: ~10-11 g.

Gradiometer mechanization

Gyro stabilized platform enables truck-based operation. Also allows for characterization of system transfer functions.

Gradiometer mounting surface

Rotation jitter

Uniform rate response Driven sinusoid response

Response obtained by actuatiing gimballed platform. Validated system transfer function.

Laser phase noise

DBR ECDL Cavity locked ECDL

Influence of laser phase noise on gravity gradient signal

Laser wavelength flluctuations result in a change in the laser phase difference read into the atomic coherences.Differential phase noise is ~ δk L, where L is the gradiometer baseline and δk is the effective propagation vector fluctuation.

Two-photon vs. single photon configurations

2-photon transitions 1 photon transitions

Rb Sr

GW signal from relative positions of atom ensembles with respect to optical phase fronts.

GW signal from light propagation time between atom ensembles.

Laser frequency noise insensitive detector

Graham, et al., arXiv:1206.0818, PRL (2013)

• Long-lived single photon transitions (e.g. clock transition in Sr, Ca, Yb, Hg, etc.).

• Atoms act as clocks, measuring the light travel time across the baseline.

• GWs modulate the laser ranging distance.

Laser noise is common

Excitedstate

Atom optics with single photon transitions

Example beamsplitter (N = 3)

• Large N realized by sequential pulses from alternating directions.

• Selectively accelerate one arm with a series of pulses

Atomic transition freq. GW phase

GW phase shift for interferometer sequence

Kinematic Noise Sensitivity

Laser noise cancels. What are the remaining sources of noise?

Relative velocity Δv between the interferometers changes the time spent in the excited state, leading to a differential phase shift.

1. Platform acceleration noise δa2. Pulse timing jitter δT3. Finite duration ∆τ οφ λασερ πυλσεσ4. Λασερ φρεθυενχψ ϕιττερ δk

Leading order kinematic noise sources:

Most severe constraint on laser frequency noise is that laser needs to be resonant with the transition (linewidth < transition Rabi freq.)

System architectures under study

1) Three satellite, Rb

2) Two satellite, Rb + atomic phase reference

3) Two satellite, Sr, single photon transition

Top level trade space is driven by strategy employed to mitigate laser frequency noise, which, if uncontrolled, will mask GW signatures.

Currently evaluating several architectures:

2 Satellite Sr Single Photon

• Single baseline (two satellites)

• Single photon atom optics (e.g., Sr) for laser and satellite acceleration noise immunity

• Atoms act as clocks, measuring the light travel time across the baseline

3 Satellite Rb

• Conventional, proven atom optics (Rb atom)

• Three satellites allow TDI for compensation of laser frequency noise.

• AI accelerometers to measure satellite vibration noise, which leads to laser frequency noise due to the Doppler effect.

2 Satellite Rb + Atomic Reference

• Conventional, proven atom optics (Rb atom)

• Single baseline (two satellites)

• Atomic frequency reference (e.g., Sr) for laser noise tracking

• AI accelerometers to measure satellite vibration noise

Rb Triangle Rb Single Arm Sr Single Arm

•Sat. acceleration noise (longitudinal)

AI accelerometer; 10-13 g/Hz1/2

AI accelerometer; 10-13 g/Hz1/2 10-8 g/Hz1/2

•Transverse position jitter 10 nm/Hz1/2

• 10 nm/Hz1/2 10 nm/Hz1/2

•Spatial wavefront λ/100 λ/100 λ/100

•Atom cloud temperature 100 pK

• 100 pK 1 pK

•Pointing stability • 0.1 μrad 0.1 μrad 0.1 μrad•Magnetic fields • 0.1 nT/Hz1/2 0.1 nT/Hz1/2 4 nT/Hz1/2•Laser phase noise • 10 kHz/Hz1/2

(TDI)• Atomic phase

reference• 10 Hz linewidth;

100 kHz/Hz1/2•Atom optics • 100 ħk • 100 ħk • 100 ħk•Formation flying • 3 satellites • 2 satellites • 2 satellites•Atom source • 108/s Rb 108/s Rb 108/s Sr

Requirements

Risk

•Noise source •Risk•Magnetic Fields •Low•AC Stark •Low•Laser intensity jitter •Low•Atom source velocity jitter •Mid•Laser pointing jitter •Mid•Solar radiation •Low•Blackbody •Low•Atom flux •Low•Laser wavefront noise •High?•Atom detection noise •High?•Gravity gradient •Mid

See analysis in Graham, et al., arXiv:1206.0818, PRL (2013) (and references therein).

Technology development for GW detectors

1) Large wavepacket separation (meter scale)

2) Ultra-cold atom temperatures (picoK)

3) Spatial wavefront noise characterization

4) Laser frequency noise mitigation strategies

30

DARPA QuASAR SBOC-1/Optical clock

AOSense 408-735-9500AOSense.comSunnyvale, CA

6 liter physics package.

Contains all lasers, Sr source, 2D MOT, Zeeman slower, spectrometer, pumps, and 3 W Sr oven; 4e10 cold a/sec.

As built view with front panel removed in order to view interior.

Sr (Yb, Hg, Ca….) GW+ mission

• GW detection at LISA sensitivity levels– One satellite pair only– Manageable attitude and vibration control– Ground based system validation

• With two isotopes/species at each satellite– Magnetic field mitigation– Equivalence principle

• With clock functionality and appropriate orbits– Time transfer

Next steps• Identify orbits• Species trades• Refined error analysis• Community TRL assessment• Community mission roadmap ….

Stochastic GW signals

CollaboratorsNASA GSFC

Babak SaifBernard D. Seery Lee FeinbergRitva Keski-Kuha

Stanford Jason HoganSusannah DickersonAlex SugarbakerSheng-wey ChiowTim KovachyPatrick MedleyDavid Berryreiser

Theory:Peter GrahamSavas DimopoulosSurjeet Rajendran

Former members:David Johnson Mike Minar

Visitors:Philippe Bouyer (CNRS)Jan Rudolf (Hannover)