General-dyne unravelling of a thermal master equation

TL;DR

This paper investigates the unravelling of a thermal quantum optical master equation through general-dyne detection, deriving the associated stochastic master equation and proposing a feasible measurement scheme for various parameters.

Contribution

It provides a detailed derivation of the stochastic master equation for thermal environments and introduces a practical measurement scheme for general-dyne detection at any parameter value.

Findings

Derived the stochastic master equation for thermal environments.

Expressed the general-dyne POVM in terms of non-hermitian eigenstates.

Proposed a feasible measurement scheme for general-dyne detection.

Abstract

We analyse the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-hermitian operator associated to the general-dyne measurement. Then, we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme which reproduces general-dyne detection for any value of the parameter characterising the stochastic master equation.