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 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

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

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

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

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))

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 ?

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).

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

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

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

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, ….

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

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

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

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.

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

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.

Transportable Gradiometer System Interference fringes Completed Physics Package

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.

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.

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.