Switching Dynamics of Metastable Open Quantum Systems

Abstract

Classical metastability manifests as noise-driven switching between disjoint basins of attraction and slowing down of relaxation, quantum systems like qubits and Rydberg atoms exhibit analogous behavior through collective quantum jumps and long-lived Liouvillian modes with a small spectral gap. Though any metastable mode is expected to decay after a finite time, stochastic switching persists indefinitely. Here, we elaborate on the connection between switching dynamics and quantum metastability through the lens of the large deviation principles, spectral decomposition, and quantum-jump simulations. Specifically, we distinguish the trajectory-level noise-induced metastability (stochastic switching) from the spectrum-level deterministic metastability (small Liouvillian gap) in a Markovian open quantum system with bistability. Without stochastic switching, whether a small spectral gap leads to slow relaxation depends on initial states. In contrast, with switching, the memory of initial conditions is quickly lost, and the relaxation is limited by the rare switching between the metastable states. Consistent with the exponential scaling of the Liouvillian gap with system size, the switching rates conform to the Arrhenius law, with the inverse system size serving as the nonequilibrium analog of temperature. Using the dynamical path integral and the instanton approach, we further extend the connection between the quasipotential functional and the probabilities of rare fluctuations to the quantum realm. These results provide new insights into quantum bistability and the relaxation processes of strongly interacting, dissipative quantum systems far away from the thermodynamic limit.