Quantum enhanced sensing with nonlinear readout in spinor Bose-Einstein condensate

Quantum metrology utilizes entanglement to enhance the signal-to-noise ratio in measurements. The conventional approach involves reducing measurement noise using entangled states, which often requires low-noise detection. An alternative strategy amplifies the signal instead, employing nonlinear interferometry with a nonlinear 'path' splitter and recombiner. Typically, the latter is the time reversal of the former, facilitating efficient detection. However, implementing time-reversed nonlinear dynamics in a general many-body system poses challenges. Here, we demonstrate two methods to realize nonlinear interferometry without invoking time reversal. In the first part of this presentation, we introduce the concept of cyclic nonlinear interferometry, which leverages the quasi-periodic spin dynamics in a three-mode ⁸⁷Rb atom spinor condensate, resulting in a metrological gain of 5 decibels over the classical limit for a total of 26500 atoms. In the second part, we further enhance the metrological gain to 16.6 dB for phase sensing in a Ramsey-like interferometer by generating and echoing spin-nematic squeezing. Our results highlight the many-body coherence of spin mixing dynamics in spinor Bose condensates and point to their possible quantum metrological application in atomic magnetometers and matter-wave interferometers.