Temporal Interference from Topological Transitions in Monitored Quantum Dynamics

Temporal interference patterns can be detected with stroboscopic monitoring that treats the back action of measurements and the unitary dynamics. Previous work established that the mean detected recurrence time is integer-quantized and given by a topological invariant, a winding number $w$. When measurement periods are at resonance with the system's timescales, the winding number can abruptly change. We focus on a generic quantum system and the transition $w\to w-2$, signified by the creation of two dark states in Hilbert space, whose corresponding modes are responsible for the interference pattern. Close to the transition an extremely slow decay of the amplitude of first detection is found, superimposed by oscillations, in contrast to the monotonically exponential decay close to the case $w\to w-1$. We show how these oscillations are obtained from the symmetry of the system and find the conditions for optimal observations of the phenomenon.