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  • Open Access

Noisy Atomic Magnetometry with Kalman Filtering and Measurement-Based Feedback

Júlia Amorós-Binefa1,* and Jan Kołodyński1,2,†

  • *Contact author: j.amoros-binefa@cent.uw.edu.pl
  • †Contact author: jankolo@ifpan.edu.pl
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PRX Quantum 6, 030331 – Published 20 August, 2025

DOI: https://doi.org/10.1103/k7nk-lrwd

Abstract

Sensing a magnetic field with an atomic magnetometer operated in real time presents significant challenges, primarily due to sensor nonlinearity, the presence of noise, and the need for one-shot estimation. To address these challenges, we propose a comprehensive approach that integrates measurement, estimation, and control strategies. Specifically, this involves implementing a quantum nondemolition measurement based on continuous light probing of the atomic ensemble. The resulting photocurrent is then directed into an extended Kalman filter to produce instantaneous estimates of the system’s dynamical parameters. These estimates, in turn, are utilized by a linear quadratic regulator, whose output is applied back to the system through a feedback loop. This procedure automatically steers the atomic ensemble into a spin-squeezed state, yielding a quantum enhancement in precision. Furthermore, thanks to the feedback proposed, the atoms exhibit entanglement even when the measurement data are discarded. To prove that our approach constitutes the optimal strategy in realistic scenarios, we derive ultimate bounds on the estimation error applicable in the presence of both local and collective decoherence, and show that these are indeed attained. Additionally, we demonstrate that, for large ensembles, the extended Kalman filter not only reliably predicts its own estimation error in real time, but also accurately estimates spin squeezing at short timescales.

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Popular Summary

Atomic magnetometers allow one to sense magnetic fields with precisions surpassing traditional superconducting quantum interference devices, despite operating at ambient temperatures. This makes them highly versatile for a variety of applications, from medical diagnostics to probing new physics. Nonetheless, their full quantum capabilities have not been reached, with interatomic entanglement being a powerful but fragile resource still to be explored. By invoking methods of signal processing and control, we demonstrate how to leverage entanglement when operating an atomic magnetometer in real time, despite the noise it exhibits. Furthermore, with the help of quantum information tools, we prove the proposed approach to be optimal, particularly in regimes involving large atomic ensembles applicable to state-of-the-art experiments.

Thanks to the construction of an explicit quantum stochastic model for the sensor dynamics, we are able to simulate its operation and integrate into it the sophisticated techniques of real-time estimation and control. We demonstrate these to automatically steer the atomic ensemble into an entangled state that substantially enhances the sensitivity. Although the noise exhibited by the atoms deteriorates the procedure, we prove that its presence sets an ultimate limit on the performance of any potential protocol. By showing how our simulations can be extrapolated to large atomic ensembles, we show that the proposed scheme may indeed attain this limit.

Our results pave the way for atomic magnetometers to be operated in real time, while incorporating active feedback schemes. Moreover, as these are common solutions in control engineering, their implementation is within the reach of current technology.

Article Text

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PRX Quantum 6, 030331– Published 20 August, 2025
  • Received 2 April 2024
  • Revised 15 May 2025
  • Accepted 2 July 2025
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