1. 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

5. 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

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

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

8. Multiphoton Beam Splitters

9. Multiphoton Bragg diffractionE k

10. 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

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

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

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

14. 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).

15. >5W injection locked Ti:sapphire laser
Reliable: re-locks automatically
Pump: 10-W Verdi & 16-W Ar+

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

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

21. 18 photon vs. 2 photon RB Interferometer
9th order Interferometer: Data
1st order
Fit

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

23. Common-mode rejection of vibrations

24. Simultaneous conjugate Interferometers

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

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

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

28. 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.

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

30. 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

31. 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.

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

33. 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

34. 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%

35. h/MCs , a, and testing quantum electrodynamics.

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

37. Photon recoil

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

39. Mission Impossible Frequency 351 725 718 47 400 Hz
Doppler width Hz
Natural linewidth Hz
Recoil shift Hz
1ppb accuracy goal: Hz

40. Simultaneous conjugate Interferometers

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

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

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

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

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

46. 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…

47. 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,

48. 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

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

50. A wild speculation.

51. 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~ Hz (de Broglie)
Atom interferometer

52. AMO group at Stanford

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

54. 12 photons: center of the fringe
36% contrast
(50% Maximum)

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

56. 18 photon interferometer
T=1ms
Contrast 12% (theoretical maximum is 25%)
Corresponds to 3months of continuous data with n=1

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

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

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