Multiple-scale analysis of open quantum systems

Highlights: • We developed a perturbation technique for the study of open quantum systems. • The technique uses multiple-scale analysis to solve time-local master equations. • We obtain analytical approximations to the temporal evolution of the density matrix. • The method is easy to implement and suitable for a wide range of perturbations. -- Abstract: In this work, we present a multiple-scale perturbation technique suitable for the study of open quantum systems, which is easy to implement and in few iterative steps allows us to find excellent approximate solutions. For any time-local quantum master equation, whether markovian or non-markovian, in Lindblad form or not, we give a general procedure to construct analytical approximations to the corresponding dynamical map and, consequently, to the temporal evolution of the density matrix. As a simple illustrative example of the implementation of the method, we study an atom-cavity system described by a dissipative Jaynes-Cummings model. Performing a multiple-scale analysis we obtain approximate analytical expressions for the strong and weak coupling regimes that allow us to identify characteristic time scales in the state of the physical system.