Lindblad master equations for quantum systems coupled to dissipative bosonic modes

TL;DR

This paper introduces a general method using a Schrieffer-Wolff transformation to derive Lindblad master equations for quantum systems coupled to dissipative bosonic modes, enabling accurate modeling of complex quantum dynamics.

Contribution

The authors develop a novel formalism to eliminate bosonic modes and derive effective Lindblad equations, improving the description of dissipative quantum systems beyond existing methods.

Findings

Accurately predicts the Dicke phase transition.

Captures quantum metastability beyond mean-field.

Shows good agreement with exact numerical methods.

Abstract

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability beyond the mean-field approximation.