Stochastic Schr\"odinger equations with coloured noise

TL;DR

This paper extends white noise quantum trajectory theory to include non-Markovian effects using Ornstein-Uhlenbeck coloured noise, deriving stochastic Schr"odinger equations that unravel non-Markovian master equations.

Contribution

It introduces a non-Markovian extension of quantum trajectories with coloured noise and derives associated stochastic Schr"odinger equations.

Findings

Recovery of random Hamiltonian evolution under certain conditions

Derivation of non-Markovian stochastic Schr"odinger equations

Unraveling of non-Markovian master equations

Abstract

A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, non-Markovian stochastic Schr\"odinger equations which unravel non-Markovian master equations are derived.