Quantum Master Equation and Filter for Systems Driven by Fields in a Single Photon State

TL;DR

This paper derives quantum master and filter equations for systems driven by single photon states, enabling better understanding and monitoring of quantum systems interacting with such non-classical fields.

Contribution

It introduces a novel derivation of master and filter equations for systems coupled to single photon fields using a quantum stochastic model.

Findings

Derived coupled equations for the quantum master and filter.

Provided an example illustrating the application of the equations.

Abstract

The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are described using a quantum stochastic unitary model, where the continuous-mode single photon state for the field is determined by a wavepacket pulse shape. The master equation is derived from this model and is given in terms of a system of coupled equations. The output field carries information about the system from the scattered photon, and is continuously monitored. The quantum filter is determined with the aid of an embedding of the system into a larger system, and is given by a system of coupled stochastic differential equations. An example is provided to illustrate the main results.