Non-perturbative treatment of non-Markovian dynamics of open quantum systems

Dario Tamascelli, Andrea Smirne, Susana F. Huelga, Martin B. Plenio

Published 2017-09-11Version 1

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment dynamics and the other a discrete mode bosonic environment resulting in a system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian states for the environment, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment undergoing a unitary evolution, our result represents a powerful, non-perturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open system dynamics.