Cyclic nonlinear interferometry with entangled non-Gaussian spin states

Abstract

We propose an efficient nonlinear readout scheme for entangled non-Gaussian spin states based on the intrinsic quasicyclic dynamics of interacting spin-$\frac{1}{2}$ systems. We focus on two well-known spin models of twist-and-turn (TNT) and two-axis-countertwisting (TACT), where the entangled non-Gaussian spin state can be generated by spin dynamics starting from unstable fixed points. In the TNT model, the non-Gaussian probe state evolves directly back to the vicinity of the initial state during the subsequent time-forward evolution for path recombining, accompanied by quantum magnification of an encoded signal and refocusing of the associated quantum noise. Based on low-order moment measurement, we find that the optimal metrological gain nearly saturates the quantum Cram\'er-Rao bound (QCRB) and follows the Heisenberg scaling. For the TACT case, the QCRB can also be nearly approached when the state converges to either of the two unstable fixed points corresponding to the initial state or its orthogonal coherent state, respectively. The latter case goes beyond previous studies where tracing back to or crossing the initial states was mostly considered. The present protocol does not require time reversal as in typical nonlinear interferometries and it also avoids complicated measurement of nonlinear observables or full probability distributions. The operational approach we discuss presents a practical way to realize high-precision and detection-noise-robust quantum metrology with entangled non-Gaussian spin states.