Learning unified control of intrinsic nonlinear spin dynamics in atomic qudits for magnetometry

Abstract

Generating and preserving metrologically useful quantum states is a central challenge in quantum-enhanced metrology. In low-field atomic magnetometry with multilevel atoms, the nonlinear Zeeman (NLZ) effect is both a resource and a limitation. It can generate internal spin squeezing within a single atomic qudit, but under fixed readout it also rotates and distorts the measurement-relevant quadrature, limiting the usable metrological gain. The problem is further complicated by the time dependence of both the squeezing axis and the nonlinear evolution itself. Here we show that reinforcement learning can transform NLZ dynamics from a source of readout degradation into a sustained metrological resource. Using only experimentally accessible low-order spin moments, a trained agent identifies a unified control policy for this class of intrinsically nonlinear sensing dynamics. We illustrate the approach in the \(f=21/2\) manifold of \(^{161}\mathrm{Dy}\), where the learned policy rapidly prepares strongly squeezed internal states and stabilizes more than \(4\,\mathrm{dB}\) of fixed-axis spin squeezing under continuous NLZ evolution. Including state-preparation overhead, the learned protocol yields a single-atom magnetic-field sensitivity of \(13.9\,\mathrm{pT}/\sqrt{\mathrm{Hz}}\), approximately \(3\,\mathrm{dB}\) beyond the standard quantum limit. Our results establish learning-based control as an experimentally feasible route for converting unavoidable intrinsic nonlinear dynamics in multilevel atomic sensors into operational metrological advantage.