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arXiv:2607.27045

Temporal Interference from Topological Transitions in Monitored Quantum Dynamics

Qingyuan Wang, Ruoyu Yin, Eli Barkai

cond-mat.stat-mechquant-phSubmitted Jul 29, 2026• Announced Jul 30, 2026• 0 citations• Revised Oct 16, 2026 (v2)
v1 · Jul 29, 2026v2 · Oct 16, 2026
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Abstract

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.

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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.
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Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large. In addition, we show that the probability distributions over transition times have unusual asymmetric form in cases of unstable trajectories. We investigate in detail three types of processes related to unstable semiclassical dynamics. First, we analyze recently proposed mechanism of multidimensional tunneling where transitions proceed by formation and subsequent decay of classically unstable ``states.'' The second class of processes includes one-dimensional activation transitions due to energy dispersion. In this case the semiclassical transition-time distributions have universal form. Third, we investigate long-time asymptotics of transition-time distributions in the case of overbarrier wave packet transmissions. We show that behavior of these asymptotics is controlled by unstable semiclassical trajectories which linger near the barrier top.
The evolution of a quantum system comprises two fundamental processes--continuous unitary dynamics and stochastic measurement-induced jumps. The latter are often viewed as a source of decoherence. Can two histories of such an evolution, made up of local measurements, interfere with each other? Here, we answer this question in the affirmative. A manifestation of this interference is the generation of entanglement between two parts of the system that are individually coupled to distinct detectors. Specifically, we develop a protocol in which two alternative local measurement processes act on a pair of qubits, and show how interference of histories is generated under coherent control, leading to entanglement. Furthermore, we find that averaging over the detectors' readouts still results in an entangled (albeit not maximally entangled) state. Our results extend the notion of quantum interference beyond unitary evolution to genuinely measurement-driven dynamics, and identify limits on the generation of quantum correlations using interference of measurement histories.
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