1. Prospects for gravitational wave detection with atom interferometry
Seoul National University
Seoul, Korea
Jason Hogan
Stanford University
January 17, 2013

2. Topics Atom interferometry Gravitational wave in a 10 meter tower
detection with atoms

3. Cold Atom Inertial Sensors
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
Technology evolution:
AOSense commercial AI gravimeter (2011)
AI gyroscope (1997)
AI compact gyroscope (2008)

4. 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

5. 10 m Accelerometer Sensitivity
10 m atom drop tower
2T ~ 2.3 s
K eff = 2k
Shot noise limited 107 atoms per shot:
rad
(~ 1 month)
State of the art:
“LMT” beamsplitters with
= k
[S Chiow et al., Phys. Rev. Lett. 107, (2011).]

6. 2T = 2.3 s: Images of Interferometry
Atom Interferometry
Design Goal: g Test of the Equivalence Principle
t = T: Image at apex
1.5 cm
F=1
F=2
F=1
F=2
(pushed)
1 cm
2T = 2.3 s: Images of Interferometry
≈ 4 mm/s
~ 10 m
2.3 s

7. Apparatus Ultracold atom source Optical Lattice Launch
>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

8. Beam Angle Phase
Phase imprinted by beam angle (small ):
Position: g

9. Coriolis Phase Phase imprinted by beam angle (small ):
Uniform Rotation Rate
Coriolis:
Coriolis Effect
Gustavson et al. PRL 78, 1997
McGuirk et al. PRA 65, 2001
Hogan et al. Enrico Fermi Proceedings, 2009
Lan et al. PRL 108, 2012

10. Coriolis Phase Phase imprinted by beam angle (small ):
Uniform Rotation Rate Coriolis:
Coriolis Compensation
Gustavson et al. PRL 78, 1997
McGuirk et al. PRA 65, 2001
Hogan et al. Enrico Fermi Proceedings, 2009
Lan et al. PRL 108, 2012

11. Rotation Compensation System
In-vacuum nanopositioning stage & mirror
< 1 nrad measured precision
~ 1 nrad repeatability
Piezoresistive position sensors
Rigidly anchored to quiet floor
nanopositioner (x3)
mirror
Coarse alignment
Anchor plate

12. Single-shot Phase & Contrast
60 μrad misalignment at final pulse
F = 2
(pushed)
F = 1
F = 1 g g
F = 2
(pushed)
1 cm
1 cm
≈ 4 mm/s

13. Single-shot Phase & Contrast
60 μrad misalignment at final pulse
F = 2
(pushed)
F = 1
F = 1 g g
F = 2
(pushed)
1 cm
1 cm
≈ 4 mm/s

14. Single-shot Phase & Contrast
60 μrad misalignment at final pulse
F = 2
(pushed)
F = 1
F = 1 g g
F = 2
(pushed)
1 cm
1 cm
≈ 4 mm/s

15. Single-shot Phase & Contrast
60 μrad misalignment at final pulse
F = 2
(pushed)
F = 1
F = 1 g g
F = 2
(pushed)
1 cm
1 cm
≈ 4 mm/s

16. Spatial Frequency vs Phase Shear
θ (μrad) Spatial Fringes
Beam angle phase: 80 40
-40
-80
Fringe spatial frequency:
+ correction for
drift time to imaging
Coriolis
Compensated

17. Application: Gyrocompassing
Beam Angle + Coriolis Error:
True north:
Precision: mdeg
Repeatability: ~ 1 mdeg
Correction to axis: deg g

18. LMT Beamsplitters: Coherent Phase Amplification
Large momentum transfer (LMT) beamsplitters – multiple laser interactions
Each laser interaction adds a momentum recoil and imprints the laser’s phase
LMT energy level diagram
Example LMT interferometer
 Phase amplification factor N

19. High Contrast LMT Atom Interferometers
Chiow, PRL (2011)
70% contrast
18% contrast
Coming Next:
LMT atom optics in 10 m tower
~1 m wavepacket separation
7 x g / shot

20. Topics Atom interferometry Gravitational wave in a 10 meter tower
detection with atoms

21. 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)

22. Gravitational Wave Phase Shift Signal
Laser ranging an atom (or mirror) that is a distance L away:
Position
Acceleration
Phase Shift:
Relativistic
Calculation:

23. 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.

24. Differential Measurement

25. 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

26. Terrestrial Configuration
Run two, widely separated interferometers using common lasers
Measure the differential phase shift
Benefits:
Signal scales with length L ~ 1 km between interferometers (easily increased)
Common-mode rejection of seismic & phase noise
Allows for a free fall time T ~ 1 s.
(Maximally sensitive in the ~1 Hz band)
(e.g., vertical mine shaft)

27. Gravity Gradient Noise Limit
Seismic noise induced strain analysis for LIGO (Thorne and Hughes, PRD 58) .
Allows for terrestrial gravitational wave detection down to
~ 0.3 Hz
Seismic fluctuations give rise to Newtonian gravity gradients which can not be shielded.

28. Projected Terrestrial GW Sensitivity

29. Satellite Configuration
Common interferometer laser
10 – 50 m
10 – 50 m
L ~ 1000 km

30. Strain Sensitivity L=106 m baseline 100 ħk 10-4 rad/Hz1/2 T =100 s
60 m booms
Space-based atom GW detector could have science potential comparable to LISA
Flexible atom optics allows for both “broadband” and “resonant” modes

31. Requirements
Analysis to determine requirements on satellite jitter, laser pointing stability, atomic source stability, and orbit gravity gradients.
J. Hogan et al., GRG 43, 7 (2011).

32. Laser frequency noise insensitive detector
All previous interferometric GW detectors need multiple baselines or ultra stable lasers.
• 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.
Excited
state
Laser noise is common
arXiv:

33. 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

34. Reduced Noise Sensitivity
Intrinsic laser noise cancels. What are the remaining sources of noise?
Any relative velocity Δv between the interferometers affects the time spent in the excited state, leading to a differential phase shift.
Leading order kinematic noise sources:
1. Platform acceleration noise da
2. Pulse timing jitter dT
3. Finite duration Dt of laser pulses
4. Laser frequency jitter dk
Differential phase shifts (kinematic noise) suppressed by Dv/c < 3×10-11

35. 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)

36. Collaborators Stanford University NASA Goddard Space Flight Center
Babak Saif
Bernard D. Seery
Lee Feinberg
Ritva Keski-Kuha
Stanford University
PI:
Mark Kasevich
EP:
Susannah Dickerson
Alex Sugarbaker
LMT:
Sheng-wey Chiow
Tim Kovachy
Theory:
Peter Graham
Savas Dimopoulos
Surjeet Rajendran
Former members:
David Johnson (Draper)
Jan Rudolf (Rasel Group)
Also:
Philippe Bouyer (CNRS)