Atom Optics for Gravitational Wave Detection Holger Müller, U.C. Berkeley Sven Herrmann, Bremen Sheng-wey Chiow, Stanford Steve Chu, U.S. Department of Energy Gallileo Gallilei Institute, Firenze 2009

Why atomic gravitational wave interferometric sensors (AGIS)? “Mirrors” are light wavefronts, linked by light cones allows for common-mode rejection of vibrations No vibration isolation necessary Distance measurement based on quantum mechanics Action of laser on atom inherent part of operation Sensitivity at 1 Hz New technology, at the beginning of a development

AGIS: example Examples: k=2π/1μ, h=10-20, ω=2π*1Hz Φ~3*10-10 n=10,000 =>Φ~3*10-6

AGIS: challenges 10,000 photon beam splitters Common-mode rejection of vibrations Atom sources Low-noise detection of atoms (Squeezing)

Multiphoton Beam Splitters

Multiphoton Bragg diffraction E k

Raman-Nath regime Short pulses (<<1/wr) Amplitudes of momentum states are Bessel functions => Very lossy n=0 2 Population 4 6 Interaction strength*interaction time

Higher-order adiabatic elimination Starting point: Adiabatic theory Re-insert into Schrodinger equation:

Bragg Regime: Square pulses Integrals easy… Population of neighbour states (losses) High losses, unless pulses extremely long

Bragg Regime: Gaussian pulses Integrals VERY hard: But can be computed using saddle point method:

Requirements ~1W per beam 40mW Good Gaussian shape (Real-time amplitude control) square Good timing not critical Low noise, ~1/n Low wavefront distortion, ~1/n not critical Low vibration, ~1/n H.M et al, PRA, in press H.M. et al, Appl. Phys. B 84, 633 (2006); Opt. Lett. 31, 202 (2006); Opt. Lett. 30, 3323 (2005).

>5W injection locked Ti:sapphire laser Reliable: re-locks automatically Pump: 10-W Verdi & 16-W Ar+

Next steps: Lattice cooling Raman Sideband Cooling Next steps: Lattice cooling

12, 20, and 24-photon Interferometry 12th order: 144 fold sensitivity 72% of opt. contrast H.M. et al., PRL 100, (2008)

18 photon vs. 2 photon RB Interferometer 9th order Interferometer: Data 1st order Fit

Visibility vs. pulse separation 2222 Problem: Contrast decay Visibility vs. pulse separation Vibration Isolation cutoff Limitation: vibrational phase noise

Common-mode rejection of vibrations

Simultaneous conjugate Interferometers

Results Results 6th order Bragg diffraction, T =1 ms

High ħk 12ħk, C=25% 20ħk, C=27% Almost no contrast reduction with higher momentum transfer

Long Pulse Separation Time Results 12ħk, T =100 ms

Long Pulse Separation Time • 50 times increase No SCIs • Contrast at large T limited by cloud expansion 2,500-fold increase in enclosed area for 20ħk.

Scalable momentum transfer: Bragg-Bloch-Bragg (BBB) beam splitter

Bloch oscillations atoms in accelerated optical lattice can transfer 1000s of ħk, very robust …but (so far) only to common momentum end-to-end coherence yet to be demonstrated

BBB splitter Bloch oscillations AC Stark effect not balanced Bragg diffraction Assymetry input/output That’s it! But: dual lattices, lattice loaded twice, and one Bragg diffraction.

Full BBB splitter Intensity vs. Time Laser difference frequency Trajectories of the atom

BBB interferometers 24 optical lattices: 4 dual 4 quadruple 6 Bragg diffractions: 2 single 2 dual. Will it be coherent? 1: dual lattice 2: single Bragg 3: quadruple lattice 4: dual Bragg

BBB interferometers 12ħk, C=17% 18ħk, C=20% …yes! End-to-end coherence of Bloch oscil-lations Might be scalable to 100s of ħk. 20ħk, C=17% 24ħk, C=15%

h/MCs , a, and testing quantum electrodynamics.

a from electron g-2 Hypothetical SUSY influence (muon g-2)

Photon recoil

a from recoil measurements 0.44ppb 0.20ppb 0.03ppb 0.007ppb

Mission Impossible Frequency 351 725 718 47 400 Hz Doppler width 300 000 000 Hz Natural linewidth 5 000 000 Hz Recoil shift 2 000 Hz 1ppb accuracy goal: 0. 000 002 Hz

Simultaneous conjugate Interferometers

Bayesian estimation to measure α 1-day run, 15,000 data points, T=100ms, 10ħk Df=3.6mrad or 6.8 10-9 Resolution in a: 3.4 ppb

Predicted h/m noise& error budget Clade Wicht This Improved by Laser noise 13 10 0.002 Multiphoton Bragg, SCIs, direct reference lock RF synthesizer 0.01 Detection (1h) 0.02 Gouy Phase -0.89(4) -8(4) <0.05 Large beams w/ high power Pointing -1.00(4) -2(2) <0.025 Interferometric stabilization Dispersion -9.8(14.0) -0.37(30) <0.15 Detuning Laser freq. 0.6 0.8 <0.2 MTS <0.01 frequency comb Gravity grad. -9.1(1.0) 0.18(2) <0.1 Direct measurement Q. Zeeman 0.098 2 <0.1 same internal states Light shift 0.02(10) (0.3) <0.1 Errors in ppb in one hour of integration time.

a from electron g-2 05/29/2009 Hypothetical SUSY influence (muon g-2)

My personal vision of the Future: Very large Area Atom Interferometers

Atomic fountain with cavity Intensity enhancement Single-atom detection Well-defined wavefronts Factor of 100-1000 further signal enhancement due to N=100-500 Bragg diffraction Tests of General Relativity, inertial sensing, navigation, a,... GP-Cs: Ultra-high resolution Sagnac interferometry, sensitive to gravitomagnetism

Summary 24 Photon beam splitters with Bragg diffraction Simultaneous conjugate interferometers: 2,500 fold enclosed area Bloch-Bragg-Bloch beam splitters: 24 photons so far, scalable to 100s of ħk Fine-structure constant 3.6ppb, more to come…

AGIS: challenges 10,000 photon beam splitters () Common-mode rejection of vibrations  Atom sources () Low-noise detection of atoms () (Squeezing) - Ultra low wavefront distortion optics () High-power, ultra-low phase noise lasers at suitable wavelengths - To, for love of truth, … forward the search Into the mysteries and marvelous simplicities Of this strange and beautiful universe, Our home. John Archibald Wheeler, 1911-2008

XUV atom interferometer Example: Lithium Can be laser cooled with standard lasers 323.3, 274, 256,… 230 nm, Isat<0.8mW/cm2 2-photon recoil velocity 0.44m/s =>m2 area possible

Undergraduate Student Thanks… PI Steve Chu Postdocs Sven Herrmann Quan Long Graduate Students Sheng-wey Chiow Alexander Senger Undergraduate Student Christoph Vo

A wild speculation.

Atom interferometry as test of the gravitational redshift? z=nħkT/M=1…10000μm gz/c2~10-19/mm T T’ Cs atoms f0=Mc2/h~3.2 1025Hz (de Broglie) Atom interferometer

AMO group at Stanford

Results for Gaussian pulses Integrals VERY hard: But can be computed using saddle point method:

12 photons: center of the fringe 36% contrast (50% Maximum)

Influence of atom temperature 0.1ms 1ms 0.2ms Temperature not critical Phase noise extremely critical Post-phase lock off

18 photon interferometer T=1ms Contrast 12% (theoretical maximum is 25%) Corresponds to 3months of continuous data with n=1

Gaussian pulses n=2 4 6 8 10 Loss after p-pulse H. Mueller et al, arXiv:0704.2627; Phys. Rev. A, in press (2008)

Bragg diffraction - supersonic neon beam - n=2,4,6 Giltner et al., PRA 52, 3966 (1995)

Lattice cooling Lattice cooling to 150nK; 2.5*10^8 atoms Original Temp. 1.2mK P. Treutlein et al, PRA 2000