Recurrence and state revival in homogeneous lattices with variable coupling

Quantum walks are a key concept in physics and have become an indispensable testbed for a host of fundamental phenomena. In this context, the effect of recurrence, i.e. the return of the "walker" (or the wave function) to its initial state, has attracted considerable interest due to its applicative potential for the coherent control of quantum walks. Recent theoretical advances along these lines have been the formulation of an approximate revival theorem for quantum walks with a quasi-periodically time-dependent coin [Phys. Rev. A 93, 032329 (2016)], and a recurrence-creating protocol [Phys. Rev. A 105, 032413 (2022)]. Here, we present a new method to identify exact recurrences and show the first photonic experimental implementation of these concepts in coupled fiber loops [Phys. Rev. Lett. 104, 050502 (2010)]. Our platform synthesizes time-encoded mesh lattices via the evolution of pulses through a pair of optical fibers of unequal length coupled by a beam splitter with variable splitting ratio. Based on an analytic proof for recurrence of quantum walks in such lattices, our findings pave the way for a generalized approach to establish state revival.