Stochastic switching is a central phenomenon in dissipative many-body systems, offering a key probe of metastability across classical and quantum regimes. Here, we unravel the connection between switching dynamics and quantum metastability through the lens of spectral decomposition, quantum-jump simulations and the large deviation principles. By establishing a direct correspondence between classical fixed points and quantum metastable states, we distinguish trajectory-level, noise-induced metastability from spectrum-level, deterministic metastability in a Markovian open quantum system with bistability. The Liouvillian gap, the steady-state occupation ratio and the observed switching rates of the metastable states all exhibit exponential scaling with system size, giving rise to a quantum analogue of the Arrhenius law, with the inverse system size serving as an effective temperature. These results provide a unified picture of quantum bistability and clarify the relaxation processes of strongly interacting, dissipative quantum systems far from the thermodynamic limit.
Stochastic switching is a central phenomenon in dissipative many-body systems, offering a key probe of metastability across classical and quantum regimes. Here, we unravel the connection between switching dynamics and quantum metastability through the lens of spectral decomposition, quantum-jump simulations and the large deviation principles. By establishing a direct correspondence between classical fixed points and quantum metastable states, we distinguish trajectory-level, noise-induced metastability from spectrum-level, deterministic metastability in a Markovian open quantum system with bistability. The Liouvillian gap, the steady-state occupation ratio and the observed switching rates of the metastable states all exhibit exponential scaling with system size, giving rise to a quantum analogue of the Arrhenius law, with the inverse system size serving as an effective temperature. These results provide a unified picture of quantum bistability and clarify the relaxation processes of strongly interacting, dissipative quantum systems far from the thermodynamic limit.
We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear stationary, before eventual relaxation toward a true stationary state at much larger times. In this work, we focus on the emergence of classical metastability, i.e., when metastable states of an open quantum system with separation of timescales can be approximated as probabilistic mixtures of a finite number of states. We find that a number of classical features follow from this approximation, for the manifold of metastable states, long-time dynamics between them, and symmetries of the dynamics. Namely, those states are approximately disjoint and thus play the role of metastable phases, the relaxation toward the stationary state is approximated by a classical stochastic dynamics between them, and weak symmetries correspond to their permutations. Importantly, the classical dynamics is observed not only on average but also at the level of individual quantum trajectories: We show that time coarse-grained continuous measurement records can be viewed as noisy classical trajectories, while their statistics can be approximated by that of the classical dynamics. Among others, this explains how first-order dynamical phase transitions arise from metastability. Finally, to verify the presence of classical metastability in a given open quantum system, we develop an efficient numerical approach that delivers the set of metastable phases together with the effective classical dynamics. Since the proximity to a first-order dissipative phase transition manifests as metastability, the theory and tools introduced in this work can be used to investigate such transitions---which occur in the large size limit---through the metastable behavior of many-body systems of moderate sizes accessible to numerics.
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how the averages of system observables change with time and quantifies how non-stationary the system is during a given time regime. By drawing an analogy with the exponential decay, we are able to further investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system is approximately stationary. While this is always the case within the initial and final regimes of the dynamics, with the system respectively approximated by its initial and asymptotic states, we show that a distinct regime of approximate stationarity may arise. In turn, we establish a quantitative description of the phenomenon of metastability in open quantum systems. The initial relaxation occurring before the corresponding metastable regime and of the long-time dynamics taking place afterwards are also characterised. Furthermore, we explain how metastability relates to the separation in the real part of the master equation spectrum and connect our approach to the spectral theory of metastability, clarifying when the latter follows. All of our general results directly translate to Markovian dynamics of classical stochastic systems.
We analyze the dynamics of metastable Markovian open quantum systems by unraveling their average dynamics into stochastic trajectories. We use quantum reset processes as examples to illustrate metastable phenomenology, including a simple three-state model whose metastability is of classical type, and a two-qubit model that features a metastable decoherence-free subspace. In the three-state model, the trajectories exhibit classical metastable phenomenology: fast relaxation into distinct phases and slow transitions between them. This extends the existing correspondence between classical and quantum metastability. It enables the computation of committors for the quantum phases, and the mechanisms of rare transitions between them. For the two-qubit model, the decoherence-free subspace appears in the unraveled trajectories as a slow manifold on which the quantum state has a continuous slow evolution. This provides a classical (nonmetastable) analog of this quantum effect. We discuss the general implications of these results, and we highlight the useful role of quantum reset processes for analysis of quantum trajectories in metastable systems. Published by the American Physical Society 2024
Open quantum systems can display metastability, with multiple long-lived states coexisting. Examples include the bistability of bright and dim manifolds in nonlinear driven resonators, or the long-lived coherent states of opposite phases in parametrically-driven systems, the building block of cat-state-based quantum computers. Metastability often emerges at system sizes where density-matrix evolution is impractical. Quantum trajectories mitigate this issue by evolving wavefunctions rather than density matrices. Metastable states then emerge as attractors towards which the system rapidly relaxes until a rare switching event brings it to another attractor. Simulating them remains costly, as one must resolve fast intra-attractor dynamics over timescales long enough to gather switching statistics. To tackle this problem, we introduce the Diagonal, Switching, and Locally Optimal Unraveling (DiSLOU) method, which combines three optimization layers: (i) Switching among locally optimal unravelings that minimize the number of quantum jumps in each metastable region. (ii) Diagonal propagation: the no-jump evolution is accelerated by diagonalizing the non-Hermitian effective Hamiltonian once per attractor. (iii) Local reduced eigenspaces: the no-jump state can be faithfully propagated in a truncated subspace of only slowly decaying eigenmodes. We benchmark DiSLOU on the driven-dissipative Kerr resonator, finding no measurable loss of accuracy and the largest speedup in the bistable regime, where standard trajectories are most expensive. We then apply the method to the more challenging problem of accurately simulating rare bit-flip events in the cat manifold emerging in a two-mode dissipatively stabilized parametric oscillator, obtaining a performance improvement of over one order of magnitude. An implementation of DiSLOU in Julia is available as an open-source package.
Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of dramatic separation of timescales due to differences between Liouvillian eigenvalues. These metastable states often have nonzero coherences that die off only in the long-time limit once the system reaches thermal equilibrium. We examine two distinct situations that give rise to this effect: one in which dissipative dynamics couple together states only within a nearly degenerate subspace, and one in which they give rise to jumps over finite-energy splittings, between nearly degenerate subspaces. We find, in each case, that a change of basis can often lead to a representation that more naturally captures the impact of the system-bath interaction than does the energy eigenbasis, revealing that separate timescales are associated with separate processes (e.g., decoherence into a nonenergy eigenbasis, decay of population correlations to the initial state). This approach is paired with the inspection of quantum trajectories, which further provide intuition as to how open system evolution is characterized when coherent oscillations, thermal relaxation, and decoherence all occur simultaneously. Published by the American Physical Society 2024
We demonstrate that fluctuation-induced bistability is a robust and generic phenomenon in strongly interacting many-body systems with strong light-matter coupling. We identify a common microscopic mechanism based on resonances between photonic transitions and many-body energy scales, unifying the emergence of fluctuation-induced bistability across a broad class of models, including interacting spins, fermions, and bosons coupled to cavity modes. We develop complementary methods to study both the steady-state properties of fluctuation-induced bistability and its dynamical formation at finite times. In particular, we introduce the dressed-state rate equation approach, which reveals rich metastable dynamics and enables the investigation of its system-size dependence. By comparing its predictions with numerically-exact tensor-network simulations, we identify signatures of fluctuation-induced bistability already in small systems on finite timescales. Our results establish fluctuation-induced bistability as a universal feature of dissipative cavity-coupled many-body systems and provide a general framework for the investigation of its non-equilibrium dynamics across a wide range of hybrid quantum platforms.