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arXiv:2303.13682 · Review of Scientific Instruments

Active stabilization of kilogauss magnetic fields to the ppm level for magnetoassociation on ultranarrow Feshbach resonances

Mateusz Borkowski, Lukas Reichsöllner, Premjith Thekkeppatt, Vincent Barbé, Tijs van Roon, N. J. van Druten, Florian Schreck

Published Jul 1, 2023• 19 citations
arXivHTMLPDF

Abstract

Feshbach association of ultracold molecules using narrow resonances requires exquisite control of the applied magnetic field. Here, we present a magnetic field control system to deliver magnetic fields of over 1000 G with ppm-level precision integrated into an ultracold-atom experimental setup. We combine a battery-powered, current-stabilized power supply with active feedback stabilization of the magnetic field using fluxgate magnetic field sensors. As a real-world test, we perform microwave spectroscopy of ultracold Rb atoms and demonstrate an upper limit on our magnetic field stability of 2.4(3) mG at 1050 G [2.3(3) ppm relative] as determined from the spectral feature.

DOI
10.1063/5.0143825

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Feshbach association of ultracold molecules using narrow resonances requires exquisite control of the applied magnetic field. Here, we present a magnetic field control system to deliver magnetic fields of over 1000 G with ppm-level precision integrated into an ultracold-atom experimental setup. We combine a battery-powered, current-stabilized power supply with active feedback stabilization of the magnetic field using fluxgate magnetic field sensors. As a real-world test, we perform microwave spectroscopy of ultracold Rb atoms and demonstrate an upper limit on our magnetic field stability of 2.4(3) mG at 1050 G [2.3(3) ppm relative] as determined from the spectral feature.
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.
Magnetic Feshbach resonances are a key tool in the field of ultracold quantum gases, but their full exploitation requires the generation of large, stable magnetic fields up to 1000 G with fractional stabilities of better than 10−4. Design considerations for electromagnets producing these fields, such as optical access and fast dynamical response, mean that electric currents in excess of 100 A are often needed to obtain the requisite field strengths. We describe a simple digital proportional-integral-derivative current controller constructed using a field-programmable gate array and off-the-shelf evaluation boards that allows for gain scheduling, enabling optimal control of current sources with non-linear actuators. Our controller can stabilize an electric current of 337.5 A to the level of 7.5 × 10−7 in an averaging time of 10 min and with a control bandwidth of 2 kHz.
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.
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.
In various leading-edge ultracold atom experiments in fields such as quantum simulation, quantum computing, and quantum precision measurement, precise and fast control of the magnetic field is important and a current source with a low noise level and high control bandwidth is required. Conventional commercial current sources, even the expensive ones, may not meet the requirements. Here, we present a battery-powered current source (BPCS) solution that has a maximum output of 100 A with a root-mean-square noise of about only 0.35 mA (integrated from 1 Hz to 3 MHz) and a control bandwidth of about 10 kHz. The large output current is sourced from a lead-acid battery, a fluxgate current sensor is used to detect the output current, and fast feedback regulation is done by using an insulated-gate bipolar transistor under the control of an analog proportional-integral controller. The battery power method eliminates the switching noise. A prepulse method is applied to shorten the settling time when the current steps down from a high level to a low level that is close to zero. These features make the BPCS a suitable analog-controlled floating current source for cold-atom experiments such as the preparation of a single 2D quantum gas and optical lattice atomic clocks.
Magnetic fields are one of the main tools for controlling the interaction of ultracold atoms using the so-called Feshbach resonances. However, the accurate knowledge of magnetic fields within the high-vacuum chamber is significantly complicated due to the inexact knowledge of the setup geometry, the presence of magnetic parts, and other. In this paper, we demonstrate precision calibration of magnetic fields in the high-vacuum setup using microwave spectroscopy of the ground state of ultracold thulium atoms.