The space cold atom interferometer for testing the equivalence principle in the China Space Station

The study targets a high-precision test of the weak equivalence principle (WEP), a central component of Einstein’s equivalence principle in general relativity, by measuring the differential acceleration of dual-species cold atoms. As general relativity and quantum mechanics remain incompatible, theories beyond the Standard Model often predict WEP violations. Prior macroscopic tests on Earth (torsion balances, lunar laser ranging) have reached ~10^-13, while satellite MICROSCOPE achieved ~10^-15. Atom interferometers enable microscopic and quantum-state-resolved tests, with the best ground-based precision at ~10^-12. Microgravity allows long interrogation times and thus higher sensitivity. The China Space Station’s Microgravity Scientific Laboratory Cabinet (MSLC) offers ~10^-7 g environment but imposes strict constraints on size and power. The authors designed a compact dual-species rubidium atom interferometer payload to exploit MSLC microgravity to advance WEP testing.

The paper contextualizes WEP testing across macroscopic and microscopic domains. Classical methods (pendulum, torsion balance, free-fall, lunar laser ranging, astronomical observations) have probed WEP to ~10^-13 on Earth. Spaceborne MICROSCOPE achieved 10^-15 using differential accelerations of concentric test masses. Atom-interferometric WEP tests began with Fray et al. (2004) using 85Rb/87Rb at ~10^-7 and have progressed across species (Rb, K, Sr), with Asenbaum et al. (2020) reaching ~10^-12 using ultracold Rb isotopes. Microgravity platforms have advanced cold-atom technologies: QUANTUS (drop tower) demonstrated MOT, BEC, and Mach–Zehnder interferometry; MAIUS (sounding rocket) demonstrated BEC production and coherence; ICE (parabolic flights) achieved Ramsey fringes and a 85Rb/39K WEP test at ~10^-4; STE-QUEST (ESA proposal) targets 10^-17 with 87Rb/41K. Space cold atom platforms like CAL and BECCAL broaden the field, and proposed missions (Q-WEP, QTEST, SAI, SAGE) aim at gravitational wave and dark energy detection with atom interferometry.

Design constraints are dictated by the MSLC’s limited volume and power while providing ~10^-7 g microgravity. The team developed a compact dual-species 85Rb/87Rb atom interferometer with three main elements. - 3D velocity selection to achieve effectively ultracold ensembles: After 3D-MOT and polarization-gradient cooling, atoms freely expand; a Raman pulse of controlled duration selects the velocity distribution along the Raman axis, and imaging/detection aperture selects transverse velocities, yielding 3D velocity selection without evaporative cooling. For N=5×10^8, Te=4 µK, r0=0.5 mm, selection half-range l=0.5 cm, and free expansion t=2.5 s, the 3D selection ratio is β3D≈5.2×10^-4, giving Nsel≈2.6×10^5 and Tsel-1D≈14 nK equivalent. - Double-diffraction Raman interferometry with phase-shear readout: A double-diffraction Raman scheme is chosen for lower temperature requirements and internal-state-resolved detection. Phase shear is applied to obtain spatial fringes in a single shot and suppress dephasing from rotation and gravity gradient. The detection geometry images fluorescence along z while the Raman beam propagates along z and is separated by a PBS. - Rotation compensation: Owing to residual, uncertain rotations of the magnetic suspension bench (MSB), a closed-loop piezoelectric mirror deflector, driven by an onboard IMU, dynamically tilts the Raman retro-mirror during the pulse sequence to compensate rotation-induced phase shear and mitigate decoherence from initial position/velocity spreads. - AC-Stark shift cancellation: Raman lasers are generated via fiber electro-optical modulators (FEOMs), producing carrier and ±1 sidebands. The team derives constraints to cancel differential AC-Stark shifts for both isotopes simultaneously and equalize effective Rabi frequencies. Optimized parameters: for 85Rb, carrier blue detuned by 986 MHz from |F=3⟩→|F′=4⟩; for 87Rb, carrier blue detuned by 404 MHz from |F=2⟩→|F′=3⟩; sideband-to-carrier intensity ratios selected to meet AC-Stark cancellation and Rabi balance while avoiding spontaneous emission and higher-order sidebands. - Payload subsystems: • Physical system: Titanium-alloy dual-region vacuum chamber (2D+ MOT source feeding 3D-MOT), ion and getter pumps (~10^-8 Pa), internal push-beam mirror with λ/4 plate, 3D-MOT beams (x and y–z planes), Raman beam along z retroreflected from a piezo-mounted mirror, three-layer permalloy magnetic shielding, fluxgate magnetometer, and integrated drivers/IMU. Laser delivery via three SMPM fibers. • Optical system: Two DFB lasers (LD1 for 85Rb, LD2 for 87Rb) stabilized using saturation absorption in isotope-specific vapor cells and FEOM locking. FEOM2/FEOM4 generate carriers and first-order sidebands for cooling, Raman, and detection; their outputs are combined and amplified by a tapered amplifier, then split via AOM into three fiber outputs (2D, 3D, Raman). Optical monitoring uses an FP cavity and photodiodes. Compact fused-quartz baseboard with miniaturized optics. • Electronic system: Power conversion from 28 V to required rails; main control for command handling, timing (AO/DO) sequences, data acquisition, and telemetry; functional circuits for laser/coil drivers, temperature control (LDs, TA, vapor cells, Rb source), and microwave generation for FEOMs and AOM. - Space experiment sequence: Laser cooling (2D-/3D-MOT, then PGC), atom interferometry with three Raman pulses (max T≈1 s limited by chamber size) including blow-away pulses and real-time mirror tilt compensation, followed by sequential fluorescence imaging of 85Rb and 87Rb (min inter-image 20 ms due to camera FPS). The WEP parameter η is inferred from the differential phase Δφ with known keff, T, and orbital g≈8.7 m s^-2. - Error budget modeling: Quantum projection and detection noise, rotation and gravity gradient effects (with IMU and mirror tilt uncertainties), second-order Zeeman shifts under magnetic shielding and coil design, residual AC-Stark effects (minimized by intensity symmetry and beam size), and wavefront aberrations of the retro-mirror are quantified (see Key Findings).

- Space deployment: Payload size 460 mm × 330 mm × 260 mm, ~37 kg, peak power ~70 W; launched on TianZhou-5 on 11/12/2022, installed in MSLC on 12/10/2022 and powered on; expected in-orbit lifetime ~2 years. MSLC microgravity level ~10^-7 g. - Effective ultracold ensemble via 3D velocity selection: For N=5×10^8, Te=4 µK, r0=0.5 mm, l=0.5 cm, t=2.5 s, computed β3D≈5.2×10^-4, Nsel≈2.6×10^5, Tsel-1D≈14 nK (equivalent), enabling long interrogation times without evaporative cooling. - Raman/AC-Stark optimization: FEOM-based Raman system with carriers blue detuned by 986 MHz (85Rb) and 404 MHz (87Rb), and optimized sideband/carrier intensity ratios to simultaneously null differential AC-Stark shifts for both isotopes and equalize effective Rabi frequencies. - Rotation compensation: IMU-driven piezo mirror tilt reduces rotation-induced phase shear variability, allowing phase-shear fringe extraction along z and mitigating decoherence from initial position/velocity offsets. - Expected WEP test precision: For 100 shots and T≈1 s, estimated uncertainty contributions (in η units): quantum projection noise ~1.2×10^-11, detection noise ~8.0×10^-12, rotation ~3.6×10^-10, gravity gradient ~6.4×10^-11, magnetic field ~1.2×10^-10, AC-Stark ~3.4×10^-15, wavefront aberration ~1.0×10^-14; total combined uncertainty ~4.0×10^-10, dominated by rotation and magnetic field terms. - Ground validation: 3D-MOT atom number >2×10^8; 1D temperature ~4 µK after PGC. Demonstrated double-diffraction Raman interference with phase-shear imaging using PCA (38-image sets), showing clear fringes only when the Raman is on resonance and the mirror deflector is driven at proper rate. Low fringe contrast attributed to gravity-induced spatial variation across pulses, background from single-photon pumping, and limited ability to set optimal deflector angles at short interrogation times. - Improvement pathways: With >10^4 images over mission lifetime, averaging reduces quantum and detection noise; second-order Zeeman effects can be reduced via state reversal; rotation effects reduced by more precise differential position/velocity measurement; gravity-gradient effects separable via modulation-demodulation, targeting potential η precision in the 10^-11–10^-12 range.

The work establishes the feasibility of a compact dual-species atom interferometer operating in the MSLC’s enhanced microgravity to test the WEP. By replacing evaporative cooling with 3D velocity selection, the system achieves effectively ultracold ensembles compatible with the MSLC’s tight power and volume constraints, enabling long interrogation times. The double-diffraction Raman scheme with phase-shear readout and active rotation compensation addresses primary dephasing sources in a rotating, low-gravity platform. The detailed error model indicates that, while intrinsic quantum and detection noises can be averaged down, platform rotation and residual magnetic gradients dominate the uncertainty. The instrument design and space-compatible control/optical subsystems lay the groundwork for in-orbit differential acceleration measurements between 85Rb and 87Rb. Ground tests demonstrate cooling performance and validate phase-shear interferometry, providing confidence for space operation. With advanced data acquisition and mitigation strategies (state reversal, modulation-demodulation, refined calibration of initial conditions), the mission could approach η sensitivities down to ~10^-11–10^-12, probing WEP at a competitive level for atom-based tests in space.

The authors designed, realized, launched, and commissioned a compact dual-species 85Rb/87Rb atom interferometer payload for installation in the China Space Station’s MSLC to test the weak equivalence principle. Key innovations include a 3D velocity selection approach enabling effectively ultracold ensembles without evaporative cooling, a double-diffraction Raman interferometer with phase-shear readout, and an IMU-driven piezo mirror for rotation compensation. An optimized Raman laser scheme cancels differential AC-Stark shifts for both isotopes. The modeled uncertainty indicates an expected WEP test precision on the order of 10^-10 for 100 shots, with dominance from rotation and magnetic field systematics. Ground experiments confirmed requisite cooling performance and demonstrated phase-shear interference fringes. Future work in orbit will leverage large datasets and systematic mitigation (magnetic-state reversal, modulation-demodulation, refined calibration) to further improve η precision potentially to 10^-11–10^-12 and inform the design of next-generation spaceborne atom interferometers.

- Platform and design constraints: MSLC-imposed limits on size, mass, and power restrict achievable interrogation time (chamber size-limited to ~1 s) and preclude evaporative cooling, necessitating velocity selection with reduced atom number. - Rotation control: Uncertain residual rotations of the magnetic suspension bench and finite IMU and piezo deflector precision limit rotation compensation accuracy, affecting fringe contrast and contributing dominant uncertainty. - Magnetic field control: Despite three-layer shielding and careful coil design, residual magnetic field gradients introduce second-order Zeeman shifts, contributing significant systematic uncertainty. - Gravity gradient compensation: Limited optical detuning range prevents implementing gravity-gradient compensation strategies, leaving residual gravity-gradient-induced differential phases. - Detection constraints: PBS-based separation halves fluorescence signal; camera FPS limits the minimum inter-species detection interval to ~20 ms; wavefront aberrations of the retro-mirror, though largely common-mode, can contribute small residuals. - Ground testing limitations: Schedule constraints precluded drop-tower or parabolic-flight microgravity tests; ground tests required reorientation to mitigate free-fall imaging limitations, preventing full optimization of space-intended sequences.