Temporal Interference from Topological Transitions in Monitored Quantum Dynamics

Quantum interference is conventionally associated with the coherent superposition of alternative paths. We uncover a temporal form of interference in repeatedly monitored quantum systems, appearing directly as fringes in the stochastic first-detection-time distribution. This temporal interference becomes remarkably long lived near a class of topological transitions at which a pair of dark states emerges in Hilbert space. Close to such transitions, the corresponding quasi-dark modes dominate the late-time dynamics and interfere coherently, producing pronounced temporal fringes whose decay becomes arbitrarily slow upon approaching the transition. We identify the symmetry conditions underlying this mechanism and relate the fringe frequency to the energy spectrum of the Hamiltonian. Our results reveal how the interplay of quantum superposition, topological transitions, and dark-state formation generates long-lived temporal interference in monitored quantum dynamics.