Sensitivity Scaling and Limits of Cavity Enhancement in Miniaturized Optically Pumped Magnetometers

The sensitivity of miniaturized optically pumped magnetometers (OPMs) is limited by weak atom-light coupling, which an optical cavity can enhance. In this work, we model the photon-shot-noise-limited sensitivity of cavity-enhanced OPMs in the regime of strongly collisionally broadened optical transitions, characteristic of buffer-gas-filled miniaturized vapor cells. The cavity enhancement is benchmarked against a single-pass free-induction-decay OPM employing Faraday-rotation readout, with the probe power and detuning jointly optimized using the Cramér-Rao lower bound as a figure of merit. For a Fabry-Pérot cavity, we compare side-of-fringe, homodyne, Pound-Drever-Hall, and Faraday-rotation readout. All four yield an optimal sensitivity enhancement scaling as $α\sqrt{2\mathcal{F}/π}$, where $\mathcal{F}$ is the cavity finesse and $0.5\leq α\leq 1$ is a readout-dependent prefactor. The enhancement is maximized at critical coupling, and we quantify its degradation away from this point. We further show that, despite spin-dependent absorption associated with the ensemble's vector polarizability, near-critical coupling can be maintained throughout spin precession at arbitrary finesse by exceeding a derived probe-power threshold and increasing the atomic detuning with finesse. We also establish a limit to the maximum cavity enhancement set by vector light-shift noise.