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
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
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.
We introduce jump-time unraveling as a distinct description of open quantum systems. As our starting point, we consider quantum jump trajectories, which emerge, physically, from continuous quantum measurements, or, formally, from the unraveling of Markovian quantum master equations. If the stochastically evolving quantum trajectories are ensemble-averaged at specific times, the resulting quantum states are solutions to the associated quantum master equation. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts. The resulting jump-time-averaged quantum states are then solutions to a discrete, deterministic evolution equation, with time replaced by the jump count. This jump-time evolution represents a trace-preserving quantum dynamical map if and only if the associated open system does not exhibit dark states. In the presence of dark states, on the other hand, jump-time-averaged states may decay into the dark states and the jump-time evolution may eventually terminate. Jump-time-averaged quantum states and the associated jump-time evolution are operationally accessible in continuous measurement schemes, when quantum jumps are detected and used to trigger the readout measurements. We illustrate the jump-time evolution with the examples of a two-level system undergoing relaxation or dephasing, a damped harmonic oscillator, and a free particle exposed to collisional decoherence.
This thesis considers quantum systems which interact with their surrounding environment. Specifically we consider the underlying stochastic dynamics which arise from the back-action of measurements performed in the environment. These quantum trajectories can be tracked by continuously monitoring the environment, as is now possible in modern experiments. We consider phenomena understood at the average level of the system state density matrix, and explore these at this more information rich level. This is especially relevant for experimental setups and implementation of quantum technologies. Firstly, we consider how systems exhibiting metastability behave at the level of stochastic quantum trajectories. In doing so we make comparisons to classical theories of metastability, where trajectories exhibit fast relaxation into distinct phases and slow transitions between them. We also illustrate when this phenomenology does not hold, with instead the emergence of a slow manifold in the form of a decoherence free subspace. We also highlight the useful role that quantum reset processes can play in the analysis of stochastic quantum trajectories. The dynamics of the stochastic quantum trajectories depends on the choice of environmental measurements. There are many choices which leave the average dynamics unchanged, but give different statistical ensembles of quantum trajectories. This gauge freedom of the average dynamics is well known. We derive the analogous result at the level of quantum trajectory ensembles; giving the measurement protocols which leave the generator of the stochastic trajectory dynamics unchanged. We also extend this to include joint trajectories of conditional system states and their associated measurement records, either full records or coarse-grained. Using these results on gauge freedoms of quantum trajectories, we consider the conditions under which the trajectory dynamics exhibit a weak unitary symmetry. We then consider under what conditions the joint state of the system and environment exhibit symmetric dynamics, including under various levels of dephasing. We find that the joint dynamics always features a separable symmetry directly related to that of the quantum master equation, but for quantum trajectories the corresponding symmetry is present only if the counting measurement satisfies certain conditions.
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
Metastability in open system dynamics describes the phenomena of initial relaxation to long-lived metastable states before decaying to the asymptotic stable states. It has been found in continuous-time stochastic dynamics of both classical and quantum systems. However, many cases of open quantum system dynamics are intrinsically discrete, and the evolution within each discrete time interval is described by an arbitrary quantum channel, which often cannot be generated by continuous-time master equations. Here we develop a general theory of metastability in discrete-time open quantum dynamics, described by sequential repetitive quantum channels. We apply the general metastability theory to a typical class of quantum channels on a target system, induced by an ancilla qubit with a pure-dephasing coupling to the target system and under Ramsey sequences. Interesting metastable behaviors are predicted and numerically demonstrated by decomposing the average dynamics of sequential quantum channels into stochastic trajectories. We also present examples of applications in quantum state and dynamics engineering of a target quantum system with an ancilla qubit.
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.