Nonlinear interferometry beyond classical limit facilitated by cyclic dynamics

Quantum metrology employs entanglement to improve measurement signal-to-noise ratio. The conventional approach based on reducing quantum noise with entangled states always demands low-noise detection. An alternative route magnifies signal instead by using nonlinear interferometry with nonlinear ‘path’ splitter and recombiner, typically with the latter being the time reversal of the former to facilitate efficient detection. However, it is difficult to implement time-reversed nonlinear dynamics in a general many-body system. Here, we present an idea to implement nonlinear interferometry without invoking time reversal. Instead of time-reversed evolution, we time the system’s return to the immediate vicinity of initial state based on cyclic quantum dynamics. Utilizing the quasi-periodic spin mixing dynamics in a three-mode ⁸⁷Rb atom spinor condensate, we implement such a `closed-loop' nonlinear interferometer and achieve a metrological gain of $3.87_{-0.95}^{+0.91}$ decibels over the classical limit for a total of 26500 atoms. The demonstration we present unlocks the high potential of nonlinear interferometry by allowing the dynamics to penetrate into deep nonlinear regime, which gives rise to highly entangled non-Gaussian state. Our approach for bypassing time reversal may open up new opportunities in the experimental investigation of researches that are typically studied by using time reversal protocols.