No 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.

Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by making an adiabatic elimination of the remaining components of the system. This procedure often leads to an effective master equation for the subsystem that is not in the well-known Gorini-Kossakowski-Lindblad-Sudarshan form (here called standard Lindblad form). Instead, it has a more general structure (here called generalized Lindblad form), which explicitly reveals the dissipative coupling between the various components of the subsystem. In this work, we present a set of dynamical equations for the first and second moments of the canonical variables for linear systems, bosonic and fermionic, described by master equations in a generalized Lindblad form. Our method is efficient and allows one to obtain analytical solutions for the steady state. Further, we include as a review some covariance matrix methods for which our results are particularly relevant, paying special attention to those related to the measurement of entanglement. Finally, we prove that the Duan criterion for entanglement is also applicable to fermionic systems.