Belavkin Filtering with Squeezed Light Sources

TL;DR

This paper develops a quantum filtering theory for Markovian systems with homodyne measurements involving squeezed light sources, providing explicit filtering equations and estimates for linear cavity modes.

Contribution

It extends quantum filtering to systems with squeezed light inputs and derives explicit filtering equations for linear cavity modes.

Findings

Derived the filtering equation for systems with squeezed light sources.

Provided explicit filtered estimates for linear cavity modes.

Applied theory to systems driven by Fock and squeezed noise.

Abstract

We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that, quantum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate $\pi_t (a)$ for the mode annihilator $a$ based on the homodyne quadrature observations up to time $t$.