Stochastic Schrodinger equations

TL;DR

This paper derives stochastic Schrödinger equations using quantum filtering theory to model real-time quantum state estimation of an open system interacting with an electromagnetic field, exemplified by resonance fluorescence.

Contribution

It provides a derivation of stochastic Schrödinger equations from quantum filtering theory for open quantum systems in contact with a field.

Findings

Real-time quantum state estimation via stochastic Schrödinger equations.

Application to resonance fluorescence demonstrates the method.

Framework connects quantum filtering with stochastic differential equations.

Abstract

A derivation of stochastic Schrodinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best estimate of the system's quantum state given the observations made. This estimate satisfies a stochastic Schrodinger equation, which can be derived from the quantum stochastic differential equation for the interaction picture evolution of system and field together. Throughout the paper we focus on the basic example of resonance fluorescence.