Stochastic Schrödinger equations with coloured noise

¹ Politecnico di Milano, Mathematics Department - piazza Leonardo da Vinci 32, I-20133, Milano, Italy, EU
² Istituto Nazionale di Fisica Nucleare, Sezione di Milano - Milano, Italy, EU
³ Laboratoire de Statistique et Probabilités, Université Paul Sabatier - 118, route de Narbonne, 31062 Toulouse Cedex 4, France, EU
⁴ Quantum Research Group, School of Physics and National Institute for Theoretical Physics, University of KwaZulu-Natal - Private Bag X54001, Durban 4000, South Africa

Received: 10 May 2010
Accepted: 5 July 2010

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 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.