Non-Markovian Quantum State Diffusion

A nonlinear stochastic Schrödinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unravelling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurement-like situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasi-periodic case we show the reversible decay of a ’Schrödinger cat’ state. Finally, our description of open systems is compatible with different positions of the ’Heisenberg cut’ between system and environment.