Genuine quantum trajectories for non-Markovian processes

Abstract

A large class of non-Markovian quantum processes in open systems can be formulated through time-local master equations which are not in Lindblad form. It is shown that such processes can be embedded in a Markovian dynamics which involves a time dependent Lindblad generator on an extended state space. If the state space of the open system is given by some Hilbert space $\mathcal{H}$, the extended state space is the triple Hilbert space $\mathcal{H}\otimes {\mathbb{C}}^3$ which is obtained by combining the open system with a three state system. This embedding is used to derive an unraveling for non-Markovian time evolution by means of a stochastic process in the extended state space. The process is defined through a stochastic Schrödinger equation which generates genuine quantum trajectories for the state vector conditioned on a continuous monitoring of an environment. The construction leads to a continuous measurement interpretation for non-Markovian dynamics within the framework of the theory of quantum measurement.

13 pages, 3 figures

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