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Cold Atom Interferometers and Applications as Drag-free Test Masses in Space

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. Atom Interferometer and its Applications.

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Cold Atom Interferometers and Applications as Drag-free Test Masses in Space

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  1. Cold Atom Interferometers and Applicationsas 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 gradiometerfor 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 Unitfor navigation • Inertial guidance without GPS • Precision accelerometers/gyros • Drag-free assistance • Precision measurementfor 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 Solid Earth and planetary interior modeling Earth Observatory for Climate Effects • - Lithospheric thickness, composition • - Lateral mantle density heterogeneity • - Deep interior studies • - Oscillation between core and mantle • Surface and ground water storage • Oceanic circulation • Tectonic and glacial movements • Tidal variations • Polar ice • Earthquake monitoring 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 Photon absorption process (p pulse) deflection (mirror) V=p/m p=hk after absorption atom light (p pulse)     beam splitter Superposition state (p/2 pulse) V=p/m p=hk V=0 (p/2 pulse)      +  In the light pulse scheme, photon recoils are used to split and redirect atom beams (waves).

  6. AI as an Accelerometer No acceleration, total phase shift difference is DF = 0 ; With an acceleration g, the phase difference is DF = 2kgT2 g fringes Atomic beam t where k is the laser wavenumber and T the time interval between laser pulses. p/2 pulse p pulse p/2 pulse Atom Interferometer with Light Pulses Atom-wave Mach-Zehnder Interferometer 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 Wave packet T 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.  pulse  +  pulses Cold Atom Interferometer as Accelerometer 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. resonance freq. w1 = w0 + keffv1 p pulses resonance freq. w2 = w0 + keff v2 Rabi method Dw = w2 - w1 = keff (v2-v1) = 2 keff gT, Df = DwdT = keff g T2 = 2 kR g T2 p/2 pulse p/2 pulse p/2 pulse p pulse p/2 pulse p/2 pulse p/2 pulse Ramsey method Atom Interferometer pulse sequence Atom Interferometer Gravity Gradiometer Free falling atoms (clocks) v1 t1 g Dv= g t ? t2 v2 Dv= g t

  12. Differential Accelerometer (Gravity Gradiometer) A gradiometer measures the difference in gravity, with the common local acceleration subtracted. Direct gravity measurement requires absolute vibration isolation - due to Einstein’s Equivalence Principle: the frame acceleration can not be distinguished locally from gravitational acceleration. AI1 F1= 2k(g1+a)T 2 DF12 = 2k (g1-g2) T 2 Common Raman beams 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, …. g F2= 2k(g2+a)T 2 AI2 a mirror

  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 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 Additional outer shield

  18. Raman laser beams Phase modulator AI 1 g AI 2 mirror Accelerometer Reference platform Vibration Compensation Scheme 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 with electronic phase forward correction. Phase noise without phase feedforward.

  19. Transportable Gradiometer System Interference fringes Completed Physics Package

  20. AI Gravity Measurements in Space Laser Atomic test masses 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 Laser Atomic test masses Atomic test masses 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 The large momentum transfer plays a key role. Nat does not scale with arm length; the photon shot noise should be still present.

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