Return to equilibrium for some quantum trajectories

TL;DR

This paper studies the behavior of two-level quantum systems under continuous measurement, deriving stochastic equations and proving they tend to equilibrium over time.

Contribution

It introduces a realistic discrete-time model for quantum trajectories and rigorously justifies the continuous-time stochastic Schrödinger equation, proving return to equilibrium.

Findings

Quantum trajectories are modeled in a discrete-time setup.

The continuous-time stochastic Schrödinger equation is derived from the discrete model.

Proves that these quantum systems return to equilibrium over time.

Abstract

We consider the situation of a two-level quantum system undergoing a continuous indirect measurement, giving rise to so-called "quantum trajectories". We first describe these quantum trajectories in a physically realistic discrete-time setup and we then justify, by going to the continuous-time limit, the "stochastic Schr\"odinger equation" attached to this model. We prove return to equilibrium properties for these equations.