Stochastic Schrödinger equations with coloured noise

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 Schrödinger equations which unravel non-Markovian master equations are derived. As a prototypical example, an harmonic oscillator is considered, able to emit light and with memory terms in the dynamics. The signature of the non-Markovian dynamics is seen in the spectrum of the emitted light.