We discuss the long-time behaviors of the nonlinear Schrodinger equation while being subjected to a random perturbation via Gaussian additive noise. It is well-known that, under the impact of sufficiently strong damping, the dynamics possesses a unique invariant probability measure. In this talk, we address the mixing issue and demonstrate that the solutions are attracted toward equilibrium with polynomial rates of any order. Our approach relies on a coupling strategy making use of pathwise Strichartz estimates specifically derived for the equation. This talk is based on a joint work with Kihoon Seong.