Universal Dissipationless Dynamics in Gaussian Continuous-variable Open Systems

We investigate the universal dissipationless dynamics of Gaussian continuous-variable systems in the presence of a band-gapped bosonic environment. Our results show that environmental band gaps can induce localized modes, which give rise to the dissipationless dynamics where the system behaves as free oscillators instead of experiencing a full decay in the long time limit. We present a complete characterization of localized modes, and show the existence of the critical system-environment coupling. Beyond the critical values, localized modes can be produced and the system dynamics become dissipationless. This novel dynamics can be utilized to overcome the environmental noises and protect the quantum resources in the continuous-variable quantum information.