Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.

arXiv:1205.4263Physical Review LettersOct 23, 201236 citations

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

C. Z. Cao, J. Z. Han, M. Xiong +5 more

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.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.

quant-pharXiv:2603.28421Physical Review AppliedMar 31, 20260 citations

Quantum spin squeezing

Jian Ma, Xiaoguang Wang, C. P. Sun +1 more

arXiv:1011.2978Physics ReportsSep 1, 2011846 citations

Strongly Enhanced Spin Squeezing via Quantum Control

Collin M. Trail, Poul Jessen, Ivan Deutsch

We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase matched, resulting in exponential enhancement of squeezing as a function of optical density for times short compared to the decoherence time. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. Including these imperfections, our model indicates that ∼10 dB of squeezing should be achievable with laboratory parameters.We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase matched, resulting in exponential enhancement of squeezing as a function of optical density for times short compared to the decoherence time. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. Including these imperfections, our model indicates that ∼10 dB of squeezing should be achievable with laboratory parameters.

arXiv:1004.2282Physical Review LettersNov 4, 201038 citations

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.