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arXiv:2003.08101 · New Journal of Physics

Direct control of high magnetic fields for cold atom experiments based on NV centers

Alexander Hesse, Kerim Köster, Jakob M. Steiner, Julia Michl, Vadim Vorobyov, Durga Bhaktavatsala Rao Dasari, Jörg Wrachtrup, Fred Jendrzejewski

Published Feb 1, 2021• 8 citations
arXivHTMLPDF

Abstract

Abstract In ultracold quantum gases, the interactions between the individual atoms can be controlled by applying magnetic bias fields. As magnetic field fluctuations limit the precision here, typically a feedback loop needs to be employed to regulate the current through a pair of Helmholtz coils. No commercially available magnetic field sensor allows to measure large fields directly with high enough precision, leading to many unsatisfactory solutions being used in experiments. Here, we demonstrate a direct magnetic field stabilization in a regime previously not accessible, using NV centers as the magnetic field sensor. This allows us to measure and stabilize fields of 4.66 mT down to 12 nT RMS noise over the course of 24 h, measured on a 1 Hz bandwidth. We achieve a control of better than 1 ppm after 20 min of integration time, ensuring high long-term stability for experiments. This approach extends direct magnetic field control to strong magnetic fields, which could enable new precise quantum simulations in this regime.

DOI
10.1088/1367-2630/abe1e5

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Abstract In ultracold quantum gases, the interactions between the individual atoms can be controlled by applying magnetic bias fields. As magnetic field fluctuations limit the precision here, typically a feedback loop needs to be employed to regulate the current through a pair of Helmholtz coils. No commercially available magnetic field sensor allows to measure large fields directly with high enough precision, leading to many unsatisfactory solutions being used in experiments. Here, we demonstrate a direct magnetic field stabilization in a regime previously not accessible, using NV centers as the magnetic field sensor. This allows us to measure and stabilize fields of 4.66 mT down to 12 nT RMS noise over the course of 24 h, measured on a 1 Hz bandwidth. We achieve a control of better than 1 ppm after 20 min of integration time, ensuring high long-term stability for experiments. This approach extends direct magnetic field control to strong magnetic fields, which could enable new precise quantum simulations in this regime.
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.
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.
A ultralow noise magnetic field is essential for many branches of scientific research. Examples include experiments conducted on ultracold atoms, quantum simulations, and precision measurements. In ultracold atom experiments specifically, a bias magnetic field will often serve as a quantization axis and be applied for Zeeman splitting. As atomic states are usually sensitive to magnetic fields, a magnetic field characterized by ultralow noise as well as high stability is typically required for experimentation. For this study, a bias magnetic field is successfully stabilized at 14.5 G, with the root mean square value of the noise reduced to 18.5 μG (1.28 ppm) by placing μ-metal magnetic shields together with a dynamical feedback circuit. Long-time instability is also regulated consistently below 7 μG. The level of noise exhibited in the bias magnetic field is further confirmed by evaluating the coherence time of a Bose-Einstein condensate characterized by Rabi oscillation. It is concluded that this approach can be applied to other physical systems as well.
Accurate control of magnetic fields is crucial for cold-atom experiments, often necessitating custom-designed control systems due to limitations in commercially available power supplies.Here, we demonstrate precise and flexible control of a static magnetic field by employing a field-programmable gate array and a feedback loop.This setup enables us to maintain exceptionally stable current with a fractional stability of 1 ppm within 30 s.The error signal of the feedback loop exhibited a noise level of 10 -5 A•Hz -1/2 for control bandwidths below 10 kHz.Utilizing this precise magnetic field control system, we investigate the second-order Zeeman shift in the context of cold-atom coherent population-trapping (CPT) clocks.Our analysis reveals the second-order Zeeman coefficient to be 574.21Hz/G 2 , with an uncertainty of 1.36 Hz/G 2 .Consequently, the magnetic field stabilization system we developed allows us to achieve a second-order Zeeman shift below 10 -14 , surpassing the long-term stability of current cold-atom CPT clocks.
We demonstrate a minimally-destructive in situ technique for measuring and stabilizing slowly-drifting magnetic fields in ultracold-atom experiments. While conventional magnetic-field sensors such as Hall, giant magnetoresistive, or fluxgate-based devices are broadly used, their accuracy, precision and dynamic range can be limited. In addition, these sensors are typically positioned at least several centimeters away from the in-vacuum atomic system, as their operation creates perturbing magnetic fields, and their placement is limited by geometric constraints imposed by the vacuum system. We overcome these issues by using the atomic system itself as a built-in magnetometer. To that end, we employ a pair of weak measurements to determine the Zeeman splitting -- and thereby the magnetic field -- of a magnetically sensitive atomic transition. We provide closed-form expressions quantifying the trade-offs between measurement noise, dynamic range, and atom loss. This procedure is demonstrated with ultracold Rb-87, weakly measured using partial-transfer absorption imaging. We then incorporate a Kalman filter to stabilize the magnetic field; this eliminated long-term drift in the ambient field (as high as ~70 nT/hr) in exchange for a modest increase in shot-to-shot variability from 1.8(2) nT to 2.0(2) nT.
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.