Theory of classical metastability in open quantum systems

Macieszczak, Katarzyna; Rose, Dominic C.; Lesanovsky, Igor; Garrahan, Juan P.

doi:10.1103/physrevresearch.3.033047

Cited by 39 publications

(52 citation statements)

References 106 publications

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“…The dynamics of the three-level system in the shelving configuration has been further shown in Refs. [73,74] to display signatures of metastability. In this Subsection we explore the effect of the introduction of stochastic resetting on top of the aforementioned shelving dynamics.…”

Section: Three-level Atomic Systemmentioning

confidence: 99%

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Perfetto,

Carollo,

Lesanovsky

2021

Preprint

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We consider Markovian open quantum systems subject to stochastic resetting, which means that the dissipative time evolution is reset at randomly distributed times to the initial state. We show that the ensuing dynamics is non-Markovian and has the form of a generalized Lindblad equation. Interestingly, the statistics of quantum-jumps can be exactly derived. This is achieved by combining techniques from the thermodynamics of quantum-jump trajectories with the renewal structure of the resetting dynamics. We consider as an application of our analysis a driven two-level and an intermittent three-level system. Our findings show that stochastic resetting may be exploited as a tool to tailor the statistics of the quantum-jump trajectories and the dynamical phases of open quantum systems.

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Section: Three-level Atomic Systemmentioning

confidence: 99%

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Perfetto,

Carollo,

Lesanovsky

2021

Preprint

Self Cite

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show abstract

“…Metastable manifold -The existence of eigenvalues with small real parts, which are well separated from the rest of the spectrum for small α gives rise to metastability [45,[52][53][54]. The evolution ρ(t) = e tL ρ 0 of any initial state ρ 0 can be written in terms of the eigenvalues λ m and right eigenmatrices R m of the Liouvillian,…”

mentioning

confidence: 99%

“…This is the metastable regime where dynamics is approximately restricted to the lower dimensional MM. The valid combinations of c i classify a MM as either classical or quantum [45,54]. A MM is called classical if there exists a basis of density matrices ρi so that any state in the MM is a positive linear combination ρ(t) ≈ m i=1 p i ρi with 0 ≤ p i ≤ 1.…”

mentioning

confidence: 99%

“…To test for classicality of the MM we apply the algorithmic approach of Refs. [53,54] which tries to systematically find the best possible simplex from spectral data of the Liouvillian. Accuracy is measured by a bound on the average distance of metastable states outside this optimal simplex.…”

mentioning

confidence: 99%

“…These eigenvalues reside between 0 and 1 if the MM is exactly a simplex, and thus classical. How far any eigenvalues λ (Pm) j of the Pm are outside of this range defines a classicality measure [54]…”

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confidence: 99%

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Random matrix theory for quantum and classical metastability in local Liouvillians

Li,

Rose,

Garrahan

et al. 2021

Preprint

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We consider the effects of strong dissipation in quantum systems with a notion of locality, which induces a hierarchy of many-body relaxation timescales as shown in [Phys. Rev. Lett. 124, 100604 (2020)]. If the strength of the dissipation varies strongly in the system, additional separations of timescales can emerge, inducing a manifold of metastable states, to which observables relax first, before relaxing to the steady state. Our simple model, involving one or two "good" qubits with dissipation reduced by a factor α < 1 compared to the other "bad" qubits, confirms this picture and admits a perturbative treatment.

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Exact multistability and dissipative time crystals in interacting fermionic lattices

Alaeian

Buča

2022

Commun Phys

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The existence of multistability in quantum systems beyond the mean-field approximation remains an intensely debated open question. Quantum fluctuations are finite-size corrections to the mean-field as the full exact solution is unobtainable and they usually destroy the multistability present on the mean-field level. Here, by identifying and using exact modulated dynamical symmetries in a driven-dissipative fermionic chain we exactly prove multistability in the presence of quantum fluctuations. Further, unlike common cases in our model, rather than destroying multistability, the quantum fluctuations themselves exhibit multistability, which is absent on the mean-field level for our systems. Moreover, the studied model acquires additional thermodynamic dynamical symmetries that imply persistent periodic oscillations, constituting the first case of a boundary time crystal,to the best of our knowledge, a genuine extended many-body quantum system with the previous cases being only in emergent single- or few-body models. The model can be made into a dissipative time crystal in the limit of large dissipation (i.e. the persistent oscillations are stabilized by the dissipation) making it both a boundary and dissipative time crystal.

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Theory of classical metastability in open quantum systems

Cited by 39 publications

References 106 publications

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Random matrix theory for quantum and classical metastability in local Liouvillians

Exact multistability and dissipative time crystals in interacting fermionic lattices

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