Quantum Dynamic Control of a Time Dependent Mass Parametric Oscillator via Lie Algebra Representation*

The Generalized Caldirola Kanai system is an oscillator subject to the time dependent manipulation of both its frequency and mass. Here, using Lie Algebra representation techniques we analyze how to completely control this system using an arbitrary parameter variation coupled with times of rest. Specifically, we can control the squeezing of coherent states using this procedure. Furthermore, it is found that any perturbation on this system can be reversed by repeating that perturbation at an opportune time.