Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale

Abstract: A new approach to the theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly small on wide time intervals: the occupation of the virtual cloud of quanta. By "virtual" we denote those bath excitations which were emitted by the system, but eventually will be reabsorbed before any measurement of the bath state. A favourable property of the virtual cloud is that the number of its quanta is expected to saturate on long times, since physically this cloud is a (retarded) polarization of the bath around the system. Therefore, the joint state of open system and of virtual cloud (the dressed state) can be accurately represented in a truncated basis of Fock states, on a wide time scale. At the same time, there can be arbitrarily large number of observable quanta, especially if the open system is under driving. However, by employing a Monte Carlo sampling of the measurement outcomes of the bath, we can simulate the dynamics of the observable quantum field. In this work we consider the measurement with respect to the coherent states, which yields the Husimi function as the positive (quasi)probability distribution of the outcomes. The evolution of dressed state which corresponds to a particular fixed outcome is called the dressed qauntum trajectory. Therefore, the Monte Carlo sampling of these trajectories yields a stochastic simulation method with promising convergence properties on wide time scales.