Noisy atomic magnetometry in real time

Abstract

Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing, they attain a quantum-enhanced scaling of sensitivity both as a function of time, $t$, and the number of atoms involved, $N$. In our work, we rigorously study how such conclusions based on Kalman filtering methods change when inevitable imperfections are taken into account: in the form of collective noise, as well as stochastic fluctuations of the field in time. We prove that even an infinitesimal amount of noise disallows the error to be arbitrarily diminished by simply increasing $N$, and forces it to eventually follow a classical-like behaviour in $t$. However, we also demonstrate that, "thanks" to the presence of noise, in most regimes the model based on a homodyne-like continuous measurement actually achieves the ultimate sensitivity allowed by the decoherence, yielding then the optimal quantum-enhancement. We are able to do so by constructing a noise-induced lower bound on the error that stems from a general method of classically simulating a noisy quantum evolution, during which the stochastic parameter to be estimated -- here, the magnetic field -- is encoded. The method naturally extends to schemes beyond the linear-Gaussian regime, in particular, also to ones involving feedback or active control.

27 pages (+16 appendices), 7(+2) figures. Improved summary and conclusions, one extra appendix

References in corpus (13)

• Quantum metrology from a quantum information science perspective
• A Straightforward Introduction to Continuous Quantum Measurement
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Quantum Metrological Limits via a Variational Approach
• Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement
• Robust quantum parameter estimation: coherent magnetometry with feedback
• Optimal state estimation for cavity optomechanical systems
• Ultimate limits for quantum magnetometry via time-continuous measurements
• Prediction and retrodiction with continuously monitored Gaussian states
• Hamiltonian Design in Atom-Light Interactions with Rubidium Ensembles: A Quantum Information Toolbox
• Estimation of fluctuating magnetic fields by an atomic magnetometer
• Geometric approach to quantum statistical inference
• On metric of quantum channel spaces

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