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arXiv:2501.11375 · Review of Scientific Instruments

A simple magnetic field stabilization technique for atomic Bose–Einstein condensate experiments

S. Tiengo, R. Eid, M. Apfel, G. Brulin, Thomas Bourdel

Published Jun 1, 2025• 5 citations
arXivHTMLPDF

Abstract

We demonstrate a simple magnetic field stabilization technique in a Bose-Einstein condensate experiment. Our technique is based on the precise measurement of the current fluctuations in the main magnetic field coils and amounts to their feedforward compensation using an auxiliary coil. It has the advantage of simplicity as the auxiliary coils can be straightforwardly driven at the relevant frequencies (<1 kHz). The performances of the different components (power supply, current transducer, electronics…) are precisely characterized. In addition, for optimal stability, the ambient magnetic field is also measured and compensated. The magnetic field stability around 57 G is measured by Ramsey spectroscopy of a magnetic field sensitive radio frequency transition between two spin states of potassium 39, and the shot-to-shot fluctuations are reduced to 64(7) μG rms, i.e., at the 1 × 10-6 level. In the context of our experiment, this result opens interesting prospects for the study of three-body interactions in Bose-Einstein condensate potassium spin mixtures.

DOI
10.1063/5.0258855

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•Sep 21, 2026•0 citations
We demonstrate a simple magnetic field stabilization technique in a Bose-Einstein condensate experiment. Our technique is based on the precise measurement of the current fluctuations in the main magnetic field coils and amounts to their feedforward compensation using an auxiliary coil. It has the advantage of simplicity as the auxiliary coils can be straightforwardly driven at the relevant frequencies (<1 kHz). The performances of the different components (power supply, current transducer, electronics…) are precisely characterized. In addition, for optimal stability, the ambient magnetic field is also measured and compensated. The magnetic field stability around 57 G is measured by Ramsey spectroscopy of a magnetic field sensitive radio frequency transition between two spin states of potassium 39, and the shot-to-shot fluctuations are reduced to 64(7) μG rms, i.e., at the 1 × 10-6 level. In the context of our experiment, this result opens interesting prospects for the study of three-body interactions in Bose-Einstein condensate potassium spin mixtures.
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.
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.
Atomic physics experiments commonly use millitesla-scale magnetic fields to provide a quantization axis. As atomic transition frequencies depend on the magnitude of this field, many experiments require a stable absolute field. Most setups use electromagnets, which require a power supply stability not usually met by commercially available units. We demonstrate the stabilization of a field of 14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of >100 nT without any stabilization. The rms noise is measured using a field-dependent hyperfine transition in a single 43Ca+ ion held in a Paul trap at the center of the magnetic field coils. For the 43Ca+ “atomic clock” qubit transition at 14.6 mT, which depends on the field only in second order, this would yield a projected coherence time of many hours. Our system consists of a feedback loop and a feedforward circuit that control the current through the field coils and could easily be adapted to other field amplitudes, making it suitable for other applications such as neutral atom traps.
We demonstrate detection of a weak alternate-current magnetic field by application of the spin-echo technique to F=2F=2F=2 Bose-Einstein condensates. A magnetic field sensitivity of 12 pT/Hz/\sqrt{\mathrm{Hz}}/Hz​ is attained for an atom number of $5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ at a spatial resolution of 100 $\ensuremath{\mu}$m2{}^{2}2. Our observations indicate magnetic field fluctuations synchronous with the power supply line frequency. We show that this noise is greatly suppressed by application of a reverse phase magnetic field. Our technique is useful in order to create a stable magnetic field environment, which is an important requirement for atomic experiments which require a weak bias magnetic field.
This thesis investigates the response of coherently coupled spin-mixture Bose-Einstein condensates across a broad range of nonlinear regimes, extending from the deep-Rabi regime to the strongly nonlinear regime. On the theoretical side, collision processes induced and enhanced by strong coherent coupling are analyzed within a perturbative framework. Interaction channels arising from both mean-field and beyond-mean-field processes are identified, providing a microscopic description of the mechanisms through which few-body interactions contribute to the energy of the many-body system. On the experimental side, precise control over the interaction landscape is achieved in a 39-K spin mixture through improved stabilization of the magnetic field near 57 G, the operating point of the system. A feedforward compensation circuit is implemented to suppress magnetic-field noise, and Ramsey spectroscopy measurements demonstrate a twelvefold reduction in field fluctuations, corresponding to a residual root-mean-square noise level of a few tens of μG. This enhanced stability enables controlled measurements of the density-dependent equation of state of the coherently driven two-component condensate. As the density is increased, the system exhibits distinct interaction regimes. At low densities, the equation of state is dominated by repulsive two-body interactions. At intermediate densities, three-body contributions emerge and become increasingly relevant. At higher densities, the interaction energy shows an unusual saturation-like behavior. This behaviour reflects the nontrivial interplay between coherent coupling and interactions.