Stochastic Schrödinger Equations for Markovian and non-Markovian cases

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. Then, we 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.

27 pages, 8 figures

References in corpus (4)

• Continuous quantum measurement and Itô formalism
• Stochastic jump processes for non-Markovian quantum dynamics
• Quantum trajectories: memory and continuous observation
• Quantum continuous measurements: The stochastic Schroedinger equations and the spectrum of the output

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• Quantum dissipative systems beyond the standard harmonic model: features of linear absorption and dynamics
• Stochastic wave-function unravelling of the generalized Lindblad equation
• On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians
• Fidelity Relations in an Array of Neutral Atom Qubits -- Experimental Validation of Control Noise