Stochastic wave-function unravelling of the generalized Lindblad equation

Abstract

We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010)JMAPAQ0022-248810.1063/1.3514539]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.

Non-Markovian generalization of a stochastic Schrödinger equation for two interacting qubits

“…The key idea of the paper is a generalization of the linear Markovian SSE. There are many ways to derive the Markovian SSE directly from a microscopic model [21,22], from physical principles [20] or from the unravelling of the master equation [23]. Let us start with the Markovian master equation to derive the Markovian linear SSE which we will generalize to the non-Markovian case.…”

Disentanglement and a nonlinear Schrödinger equation

“…The effect of the added term on the dynamics of a single spin 1/2 is studied in section III. The spin's response to an applied fluctuating magnetic field is found to mimic the process of thermalization [15][16][17][18] (see section IV). Disentanglement induced by the nonlinear term is explored with two coupled spins (see section V).…”

Thermalization and disentanglement with a nonlinear Schrödinger equation

“…The effect of the added term on the dynamics of a single spin 1/2 is studied in section 3. The spin's response to an applied fluctuating magnetic field is found to mimic the process of thermalization [15][16][17][18] (see section 4). Disentanglement induced by the nonlinear term is explored with two coupled spins (see section 5).…”