Quantum-Classical Decomposition of Gaussian Quantum Environments: A Stochastic Pseudomode Model

We show that the effect of a Gaussian bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary bosonic modes ini-tially at zero temperature and classical stochastic fields. We test the method for Ohmic environments with exponential and polynomial cut-offs against, respectively, the hierarchical equations of motion and the deterministic pseudomode model, with respect to which the number of ancillary quantum degrees of free-dom is reduced. For a subset of rational spectral densities, all parameters are explicitly specified without the need for any fitting procedure, thereby simplifying the modeling strategy. Interestingly, the classical fields in this decomposition must sometimes be imaginary valued, which can have counterintuitive effects on the system properties, which we demonstrate by showing that they can decrease the entropy of the system, in contrast to real-valued fields.