Synthesising Keldysh and Lindblad - Correlated decay processes in higher order perturbation theory

Abstract

Motivated by correlated decay processes driving gain, loss and lasing in driven semiconductor quantum-dots, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms terms contribute to the system behaviour at the same order of perturbation theory, and make substantial contributions to the behaviour of the system.