Quantum filtering equations for system driven by non-classical fields

TL;DR

This paper derives quantum filtering equations for systems driven by non-classical light states, using input-output theory and quantum stochastic calculus, with applications to photon counting and quadrature measurements.

Contribution

It introduces a method to derive filtering equations for quantum systems influenced by specific non-classical light states, expanding the tools for quantum measurement and control.

Findings

Derived filtering equations for non-classical light states

Applied to vacuum-single photon and coherent state mixtures

Demonstrated stochastic evolution conditioned on measurements

Abstract

Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the non-classical states of the field: a combination of vacuum and single photon states and a mixture of two coherent states. We describe the stochastic evolution conditioned on the results of the photon counting and quadrature measurements.