Convergence of bipartite open quantum systems stabilized by reservoir engineering

TL;DR

This paper analyzes how bipartite open quantum systems can be stabilized through reservoir engineering by providing convergence conditions for Lindblad equations, with applications to multi-photon processes for cat qubit stabilization.

Contribution

It offers new sufficient conditions for the convergence of Lindblad equations in bipartite quantum systems, including cases with non-unique steady states supported on subspaces.

Findings

Derived convergence criteria for Lindblad master equations.

Applied results to multi-photon emission and absorption models.

Supported stabilization strategies for cat qubits.

Abstract

We study a generic family of Lindblad master equations modeling bipartite open quantum systems, where one tries to stabilize a quantum system by carefully designing its interaction with another, dissipative, quantum system-a strategy known as quantum reservoir engineering. We provide sufficient conditions for convergence of the considered Lindblad equations; our setting accommodates the case where steady-states are not unique but rather supported on a given subspace of the underlying Hilbert space. We apply our result to a Lindblad master equation modeling engineered multi-photon emission and absorption processes, a setting that received considerable attention in recent years due to its potential applications for the stabilization of so-called cat qubits.