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Time-reversed evolution has substantial implications in physics, includingprominent applications in refocusing of classical waves or spins andfundamental researches such as quantum information scrambling. In quantummetrology, nonlinear interferometry based on time reversal protocols supportsentanglement-enhanced measurements without requiring low-noise detection.Despite the broad interest in time reversal, it remains challenging to reversethe quantum dynamics of an interacting many-body system as is typicallyrealized by an (effective) sign-flip of the system's Hamiltonian. Here, wepresent an approach that is broadly applicable to cyclic systems forimplementing nonlinear interferometry without invoking time reversal. Inspiredby the observation that the time-reversed dynamics drives a system back to itsstarting point, we propose to accomplish the same by slaving the system totravel along a 'closed-loop' instead of explicitly tracing back its antecedentpath. Utilizing the quasi-periodic spin mixing dynamics in a three-mode$^{87}$Rb atom spinor condensate, we implement such a 'closed-loop' nonlinearinterferometer and achieve a metrological gain of $3.87_{-0.95}^{+0.91}$decibels over the classical limit for a total of 26500 atoms. Our approachunlocks the high potential of nonlinear interferometry by allowing the dynamicsto penetrate into deep nonlinear regime, which gives rise to highly entanglednon-Gaussian state. The idea of bypassing time reversal may open up newopportunities in the experimental investigation of researches that aretypically studied by using time reversal protocols.

Nonlinear interferometry beyond classical limit facilitated by cyclic dynamics