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arXiv:2610.21801

Three-axis Active Magnetic Compensation with Spatial Feedforward Matrix Decoupling and Hysteresis PI Regulation for Suppressing Zeeman Decoherence of Cold Atom Quantum Memories

Ya Li, Xiao-Long Zou, Xiang-Yao Liang, Chang-Qing Niu, Xin Guo, Wei-Zhe Qiao, You-Xing Chen

quant-phSubmitted Oct 15, 2026• Announced Oct 16, 2026• 0 citations
arXivHTMLPDF

Abstract

Cold-atom quantum memories require a near-zero magnetic environment (residual field <1 microtesla) to mitigate Zeeman decoherence. Conventional three-axis active compensation suffers from inter-coil crosstalk and geomagnetic drift, which degrade the uniformity and long-term stability of the zero-field region. To address this, we propose a spatiotemporally cooperative feedback-controlled suppression architecture for magnetic interference. An integrally printed three-dimensional orthogonal coil frame mechanically suppresses inter-axis flux leakage. A spatial feedforward inverse matrix is introduced to algorithmically eliminate first-order cross-coupling. A dual-threshold hysteresis incremental-PI controller filters magnetometer quantization fluctuations and avoids frequent small jitter adjustments of coil driving currents. Hardware ablation experiments, long-duration stability tests and spatial magnetic-field mapping were conducted. Experimental results show that during a 714.4 s continuous steady-hold stage, the mean and maximum residual fields at the central point reach 0.112 microtesla and 0.224 microtesla, respectively. The overlapping Allan deviations of all three components remain below 5 nT for averaging times of 1.9-178.2 s. Based on differential-ferrofluid lattice-scan measurements combined with centre-constrained quadratic vector reconstruction and soft Maxwell regularization, a weak-field spatial distribution with an RMS variation of 5.65 microtesla is fitted within a spherical region of interest of radius 5 mm, where 67.5% of the model volume meets the sub-5 microtesla coverage criterion. For a prolate ellipsoidal region matching the atomic-cloud distribution with full axis lengths of 10, 5, and 5 mm, the upper field bound within 93.7% of the volume is 2.68 microtesla.

Comments
16 pages,7 figures

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Cold-atom quantum memories require a near-zero magnetic environment (residual field <1 microtesla) to mitigate Zeeman decoherence. Conventional three-axis active compensation suffers from inter-coil crosstalk and geomagnetic drift, which degrade the uniformity and long-term stability of the zero-field region. To address this, we propose a spatiotemporally cooperative feedback-controlled suppression architecture for magnetic interference. An integrally printed three-dimensional orthogonal coil frame mechanically suppresses inter-axis flux leakage. A spatial feedforward inverse matrix is introduced to algorithmically eliminate first-order cross-coupling. A dual-threshold hysteresis incremental-PI controller filters magnetometer quantization fluctuations and avoids frequent small jitter adjustments of coil driving currents. Hardware ablation experiments, long-duration stability tests and spatial magnetic-field mapping were conducted. Experimental results show that during a 714.4 s continuous steady-hold stage, the mean and maximum residual fields at the central point reach 0.112 microtesla and 0.224 microtesla, respectively. The overlapping Allan deviations of all three components remain below 5 nT for averaging times of 1.9-178.2 s. Based on differential-ferrofluid lattice-scan measurements combined with centre-constrained quadratic vector reconstruction and soft Maxwell regularization, a weak-field spatial distribution with an RMS variation of 5.65 microtesla is fitted within a spherical region of interest of radius 5 mm, where 67.5% of the model volume meets the sub-5 microtesla coverage criterion. For a prolate ellipsoidal region matching the atomic-cloud distribution with full axis lengths of 10, 5, and 5 mm, the upper field bound within 93.7% of the volume is 2.68 microtesla.
Abstract Quantum sensors based on cold atoms are being developed which produce measurements of unprecedented accuracy. Due to shifts in atomic energy levels, quantum sensors often have stringent requirements on their internal magnetic field environment. Typically, background magnetic fields are attenuated using high permeability magnetic shielding, with the cancelling of residual and introduction of quantisation fields implemented with coils inside the shield. The high permeability shield, however, distorts all magnetic fields, including those generated inside the sensor. Here, we demonstrate a solution by designing multiple coils overlaid on a 3D-printed former to generate three uniform and three constant linear gradient magnetic fields inside the capped cylindrical magnetic shield of a cold atom interferometer. The fields are characterised in-situ and match their desired forms to high accuracy. For example, the uniform transverse field, Bx, deviates by less than 0.2% over more than 40% of the length of the shield. We also map the field directly using the cold atoms and investigate the potential of the coil system to reduce bias from the quadratic Zeeman effect. This coil design technology enables targeted field compensation over large spatial volumes and has the potential to reduce systematic shifts and noise in numerous cold atom systems.
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Many experiments involving cold and ultracold atomic gases require very precise control of magnetic fields that couple to and drive the atomic spins. Examples include quantum control of atomic spins, quantum control and quantum simulation in optical lattices, and studies of spinor Bose condensates. This makes accurate cancellation of the (generally time dependent) background magnetic field a critical factor in such experiments. We describe a technique that uses the atomic spins themselves to measure dc and ac components of the background field independently along three orthogonal axes, with a resolution of a few tens of µG in a bandwidth of ∼1 kHz. Once measured, the background field can be cancelled with three pairs of compensating coils driven by arbitrary waveform generators. In our laboratory, the magnetic field environment is sufficiently stable for the procedure to reduce the field along each axis to less than ∼50 µG rms, corresponding to a suppression of the ac part by about one order of magnitude. This suggests that our approach can provide access to a new low-field regime in cold atom experiments.
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We design and develop a high-performance magnetic shielding system for a long baseline fountain-type atom interferometer. The shielding system is achieved by a combination of passive shielding using permalloy and active compensation with coils. An 11.4 m-long three-layer cylindrical shield is completed by the process of welding, local annealing, and entire annealing. The active compensations compress the residual magnetic field to 8.0 nT max-to-min and the corresponding gradient below 30 nT/m over 10 m along the axial direction in which external compensation, internal compensation, and constant magnetic field (C-field) compensation reduce the inhomogeneities to 25.0, 12.6, and 1.7 nT (standard deviation) sequentially. We estimate that this system could reduce the systematic error of the quadratic Zeeman shift to the 10−13 level for the weak equivalence principle test with a simultaneous 85Rb–87Rb dual-species atom interferometer.
Cold atom experiments usually need a controllable and low-noise bias magnetic field to provide a quantization axis. Most labs need home-made stabilization of the field according to the actual setup, as commercially available power supply cannot directly satisfy their requirements. Here, by measuring the field fluctuations and active feedback modulating current supply of the applied magnetic field, we successfully demonstrate a field of 10.58 G with a stability to the level of 2.8 × 10−7 in a duration of 5 min. The root mean square noise is reduced to 0.05 mG, compared to the noise of 1.3 mG without stabilization. The coherence time of the magnetic-field sensitive transition between the rubidium ground states F=1,mF=−1 and 1,0, as measured by Rabi oscillation, is extended to 19.2 ms from the unstabilized value of 1.3 ms. This result is long enough for most experiments on quantum simulation and precision measurement. As our system has no passive magnetic shielding and additional compensation coils, it is highly simple and compact to provide the stable magnetic field and would be adapted to various applications with cold atoms.