Lindblad dynamics of the damped and forced quantum harmonic oscillator: General solution

TL;DR

This paper derives a general solution for the quantum harmonic oscillator under damping and forcing, modeled by a Lindblad master equation, using Lie-algebraic techniques to solve the resulting non-Hermitian Schrödinger equation.

Contribution

It introduces a Lie-algebraic method to solve the Lindblad master equation for a damped and forced quantum harmonic oscillator, providing a comprehensive analytical solution.

Findings

General solution for the density operator obtained

Method applicable to other open quantum systems

Enhanced understanding of dissipative quantum dynamics

Abstract

The quantum dynamics of a damped and forced harmonic oscillator described by a Lindblad master equation is analyzed. The master equation is converted into a matrix-vector representation and the resulting non-Hermitian Schr\"odinger equation is solved by Lie-algebraic techniques allowing the construction of the general solution for the density operator.