Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving

We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1,1) Lie algebra structure, with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.