Exponential localization of moving-end mirror in an optomechanical system

We discuss the dynamics of moving end mirror of an optomechanical system that consists of a Fabry-Perot cavity loaded with dilute condensate and driven by a single mode optical field. It is shown that quantum mechanical phenomenon of dynamical localization occurs both in position and momentum space for moving end mirror in the system. The parametric dependencies of dynamical localization are discussed. We also provide a set of parameters which makes this phenomenon experimentally feasible.