Critical Sensing with Autonomous Devices: The Self-Oscillation Threshold of a Frequency-Locked NV-Centre Magnetometer

Abstract:Feedback locking of a probe frequency to a spin resonance is the standard operating mode of precision quantum sensors. Here we deliberately operate such a lock outside its stable regime: a continuous-wave nitrogen-vacancy (NV) ensemble magnetometer, frequency-modulation (FM) locked to one flank of its optically detected magnetic resonance (ODMR), is driven through the flip (period-doubling) bifurcation of its discrete feedback map by raising the software loop gain $G$. Beyond a critical gain $\Gc$ the lock becomes a self-sustained oscillator whose limit cycle is generated by the loop itself. We derive the threshold condition $\Gc = 2\,\Dcal/\Dtrue$, which identifies the measurable content of the threshold: the ratio of the transduction slope of the ODMR lock-in signal at calibration time $D_{cal}$ to its value at present $D_{true}$. We present an identifiability analysis showing which physical parameters this single scalar can and cannot distinguish, characterize the estimators of $\Gc$ under realistic noise, and report measurements on our current setup: an experimental bifurcation diagram with onset at $\Gc \approx 2$ as predicted for a self-calibrated loop, sub-threshold critical fluctuations following the predicted $\sqrt{G/(2-G)}$ divergence.

arXiv:2607.22521 [quant-ph]

(or arXiv:2607.22521v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.22521 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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