1. Cold Atom Interferometers and Applications as Drag-free Test Masses in Space
Nan Yu
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, California 91109
Discussions with Massimo Tinto at JPL is acknowledged.

2. Atom Interferometer and its Applications
Gravity gradiometer for gravity field monitoring and 3D subsurface structure mapping
 Earth science observatory and geodesy  Deep space planetary gravity mapping and modeling  Underground structure detection  Underground resource exploration
Key points:
Atomic particle as test mass
Matter wave interferometer for high sensitivity measurement
Extremely good system intrinsic stability
Laser cooling without cryogenics ….
Inertial measurement Unit for navigation
Inertial guidance without GPS
Precision accelerometers/gyros
Drag-free assistance
Precision measurement for advancement of science
Test of Einstein’s Equivalence Principle  Frame-dragging test of the General Relativity Theory  GW and spin-gravity coupling

3. Global Gravity Field Mapping in Space
Earth Observatory for Climate Effects
Solid Earth and planetary interior modeling
Surface and ground water storage
Oceanic circulation
Tectonic and glacial movements
Tidal variations
Polar ice
Earthquake monitoring
- Lithospheric thickness, composition
- Lateral mantle density heterogeneity
- Deep interior studies
- Oscillation between core and mantle
GRACE
CHAMP
GOCE

4. Atom Interferometer Gravity Measurement in Space
Gradiometer satellite
Cold atoms
Cold atoms
GRACE and GRACE II
GOCE

5. Atom Optics: Beam Splitting and Deflection
In the light pulse scheme, photon recoils are used to split and redirect atom beams (waves).
p=hk
Photon absorption process (p pulse)
V=p/m
atom
light
after absorption
(p pulse)
    
deflection (mirror)
Superposition state (p/2 pulse)
p=hk
V=p/m
(p/2 pulse)
     +  
V=0
beam splitter

6. Atom Interferometer with Light Pulses
No acceleration, total phase shift difference is DF = 0 ;
With an acceleration g, the phase difference is
DF = 2kgT2
where k is the laser wavenumber and T the time interval between laser pulses. t
AI as an Accelerometer
Atom-wave Mach-Zehnder Interferometer
fringes
Atomic beam
p/2 pulse
p/2 pulse
p pulse
Splitter/mirror functions are accomplished by interaction with laser pulses. (M. Kasevich and S. Chu Phys. Rev. Lett. vol. 67, p.181, (1991); C. J. Borde, Phys. Lett. A, vol.140, 10 (1989))

7. Atom Wave Interference Contrast Loss
500 nm
Wave packet T
T + T
The rate of relative displacement between two separated wave packet is about 7.2 mm/s (two photon recoil).
The FWHM time width (140 us) corresponds to 504 nm spatial length over which the interference occurs.
What is this length? What determines this length? atom wave packet size or loss of coherence of the atom wave ?

8. Coherence Length and Wave Packet Size
T + T
Tvs
Longitudinal velocity selection
The longitudinal velocity: about 1 m/s, corresponds to 3 nm de Broglie wavelength.
Initial velocity selection pulse 240 s; a FWHM sinc function frequency width 5.4 kHz; a velocity group with spread v= 2.3 mm/s. This is the initial wave packet preparation, corresponding to a minimum uncertainty wave packet with spread of 450 nm (if FWHM is used as variance).
Dispersion of the atom wave packet: x(t) = (x02 + v2 t2)1/2. At the end of 2T (2 ms), the spread of the wave packet becomes 4.5 m, >> initial 0.45 m.
At the point of the interference, the wave packets mostly overlap. The coherence is determined by the initial velocity spread of the atom wave*.
* Similar observation and proof were made for neutron matter waves. Ref: Kaiser, H. S., Werner, A. and George, E. A. Phys. Rev. Lett. 50, 560 (1983). Klein, A. G., Opat, G. I., and Hamilton, W. A. Phys. Rev. Lett. 50, 563 (1983).

9. Coherence Length change as Function of Velocity Selection
Coherence Time (Length) Change in the Light Pulsed Interferometer ≈

10. Cold Atom Interferometer as Accelerometer
 pulse
 +  pulses
With over 106 detectable Cs atoms, the shot-noise limited SNR ~ 1000.
Per shot sensitivity  10-10/T2 m/s2, or about 10-11/T2 g.
Trapping and cooling
Vertical acceleration measurement. The fountain provides twice the interaction time

11. Atom Interferometer Gravity Gradiometer
resonance freq. w2 = w0 + keff v2
p pulses
resonance freq. w1 = w0 + keff v1
Rabi method
Free falling atoms (clocks) t1 v1
Dw = w2 - w1 = keff (v2-v1) = 2 keff gT,
Df = DwdT = keff g T2 = 2 kR g T2 g
Dv= g t ?
p/2 pulse
Ramsey method
p pulse
Atom Interferometer
pulse sequence
p/2 pulse t2 v2
Dv= g t

12. Differential Accelerometer (Gravity Gradiometer)
Direct gravity measurement requires absolute vibration isolation - due to Einstein’s Equivalence Principle: the frame acceleration can not be distinguished locally from gravitational acceleration.
A gradiometer measures the difference in gravity, with the common local acceleration subtracted. a
mirror g
AI1
AI2
Common Raman beams
F1= 2k(g1+a)T 2
F2= 2k(g2+a)T 2
DF12 = 2k (g1-g2) T 2
Many common mode errors are suppressed in the differential measurement to various degrees: vibration, laser phase error, AC stark shift, common optical path, magnetic fields, ….

13. Transportable Gradiometer Development
A transportable gravity gradiometer prototype with a performance goal of 2 E/(Hz)1/2 sensitivity.

14. 3D MOT Collimators and Magnetic Coils assembled
Single vacuum chamber
(1, 1, 0) launch geometry

15. Laser and Optics System
Eight injection-locked amplifiers for two 3D-MOTs and two 2D MOT sources.
Frequency tuning through phase locking of two master lasers.
Laser and optics system

16. Automation: slave injection lock control
The system uses 12 slave lasers injection-locked to a master
laser. The injection locking works within a certain range of slave laser current and temperature. This locking range can be visualized by monitoring the the slave absorption signal:
Absorption cells for locking
The slave lasers parameters drift, so they need to be repeatedly adjusted to keep the lock reliable at all times. We have developed a software utility monitoring and adjusting the locking range for all 12 slave lasers.

17. Magnetic Shields Inner Shield
Magnetic shields were designed, modeled, built and tested
Inner tube shield and double-layer of of outer shielding
Measured shielding factors:
Inner: 321
Middle: 109
Outer: 105
Inner Shield
Modeled shielding factor
Shield Separation
Shielding Factor
Trap Center
(z = 0 cm)
Top of Launch
(z = 13.8 cm)
0.5 cm
280
4000
2.0 cm
430
8250
5.0 cm
750
9070
Additional outer shield 17

18. Vibration Compensation Scheme
Reference platform
Accelerometer
Phase
modulator
AI 2 g
Raman laser beams
AI 1
mirror
Accelerometer installed below mirror for phase-feed forward compensation
Vibrations of the reference platform can be actively compensated via electronic feedback from an accelerometer mounted on the platform (F. Yver-Leduc et al., J. Opt. B 5, S140 (2003).
Phase noise without phase feedforward.
Phase noise with electronic phase forward correction.

19. Transportable Gradiometer System
Interference fringes
Completed Physics Package

20. AI Gravity Measurements in Space
Laser
Atomic test masses
Gravity gradient measurement configuration with atom interferometers. The baseline separation can be from 1 m to 100 km.
Atoms are used as true drag-free test masses
Atoms are also used as optical phase reader
Single satellite:
(L=10m) < 10-3 EU/Hz1/2
Long baseline: (100 m) < 10-4 EU/Hz1/2
Satellite formation: (100km): < x10-7 EU/Hz1/2
Gravity gradient unit: EU (Eotvos) = 10-9 m/s2 /m.

21. Space Laser Interferometers
GRACE II
Laser ranging between two drag-free spacecraft test masses. Ranging precision: nm/Hz1/2
LISA
Laser ranging between two (three) pairs of drag-free spacecraft test masses. Ranging precision: pm/Hz1/2.

22. Atomic Test Masses Extend to GW Detection
Laser wavelength λ
Shot noise limited SNR = (Nph)1/2
Phase resolution: ≈1/SNR
Ranging error: δx ≈ λ/(Nph)1/2
ΔΦ=keff a T2
keff=2π/λefff
Shot noise limited SNR = (Nat)1/2
Phase resolution: δΦ≈1/SNR
Acceleration error ≈ (1/SNR) λeff (1/T2)
Ranging error: δx ≈ δaT2 ≈ λeff /(Nat)1/2
Laser
Atomic test masses
The large momentum transfer plays a key role. Nat does not scale with arm length; the photon shot noise should be still present.