Perturbation Analysis of Quantum Reset Models

Abstract

This paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

Quadratic open quantum harmonic oscillator

“…The effect of the interaction is generally that of a disturbing noise that may be small, but it can hardly be neglected. Luckily, recent results suggest that one can also take advantage of the presence of noise in some efficient way to generate or enhance certain properties of the system states such as entanglement (see [5,6,8,15,25] and the references therein).…”

“…A strategy known as quantum reservoir engineering where the coupling to the environment provides the dissipation required for stabilization has been recently investigated ( [22]). It has been demonstrated that entangled steady states arise in the presence of dissipation for finite dimensional (mostly fermion) systems ( [6,8,15,25]).…”

“…The authors would like to thank Alain Joye who brought the problem to their attention after a seminar on the results of [15] as well as for fruitful discussions.…”

Preface: stochastic resetting—theory and applications

“…The work done on stochastic resetting was extremely diverse spanning different subjects ranging from first-passage and search theory [22][23][24][25][26][27], stochastic thermodynamics [28][29][30][31][32][33], optimization problems [34,35], quantum mechanics [5,[36][37][38], and all the way to population dynamics which can be subject to abrupt perturbations or colossal crashes that can be modeled as resetting events [39,40]. This surge in research activity called for a special issue that brings together contributions from multiple groups working on various facets of stochastic resetting.…”