A Master Equation with Generalized Lindblad Form and a Unitary Transformation by the Squeezing Operator

TL;DR

This paper applies a squeezing operator to transform a generalized Lindblad master equation into a standard form, revealing new algebraic structures and enabling approximate solutions.

Contribution

It introduces a unitary squeezing transformation to convert a generalized Lindblad master equation into the standard form, uncovering new Lie algebra structures and solutions.

Findings

Transformation simplifies the master equation to the usual Lindblad form.

New algebraic structures based on su(1,1) are identified.

Approximate solutions are constructed using the transformed algebraic framework.

Abstract

In the preceding paper arXiv:0802.3252 [quant-ph] we treated a model given by a master equation with generalized Lindblad form, and examined the algebraic structure related to some Lie algebras and constructed an approximate solution. In this paper we apply a unitary transformation by the squeezing operator to the master equation. Then the generalized Lindblad form is tranformed to the usual Lindblad one, while the (original) Hamiltonian is tranformed to somewhat complicated one. As a result we have two different representations based on the Lie algebra su(1,1). We examine new algebraic structure and construct some approximate solution.