Stochastic Schrödinger Equations for Markovian and non-Markovian Cases

Author:

Semina I.1,Semin V.1,Petruccione F.12,Barchielli A.345

Affiliation:

1. Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, 4001, South Africa

2. National Institute for Theoretical Physics (NITheP), South Africa

3. Politecnico di Milano, Dipartimento di Matematica, piazza Leonardo da Vinci 32, 20133 Milano, Italy

4. Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Milano, Italy

5. Istituto Nazionale di Alta Matematica (INDAM-GNAMPA), Italy

Abstract

Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples — the damped harmonic oscillator and a two-level atom with homodyne photodetection. We then consider how to introduce memory effects in the stochastic Schrödinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

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