Quantum resetting in continuous measurement induced dynamics of a qubit

Abstract

We study the evolution of a two-state system that is monitored continuously but with interactions with the detector tuned so as to avoid the Zeno affect. The system is allowed to interact with a sequence of prepared probes. The post-interaction probe states are measured and this leads to a stochastic evolution of the system's state vector, which can be described by a single angle variable. The system's effective evolution consists of a deterministic drift and a stochastic resetting to a fixed state at a rate that depends on the instantaneous state vector. The detector readout is a counting process. We obtain analytic results for the distribution of number of detector events and the time-evolution of the probability distribution. Earlier work on this model found transitions in the form of the steady state on increasing the measurement rate. Here we study transitions seen in the dynamics. As a spin-off we obtain, for a general stochastic resetting process with diffusion, drift and position dependent jump rates, an exact and general solution for the evolution of the probability distribution.

27 pages, 4 figures

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• Dynamically emergent correlations in bosons via quantum resetting
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Tight-binding model subject to conditional resets at random times
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Stationary state of harmonic chains driven by boundary resetting
• Spikes in Poissonian quantum trajectories
• Optimal detection of quantum states via projective measurements