Temporal Dynamics of Bose-Condensed Gases

Abstract

We perform a detailed quantum dynamical study of non-equilibrium trapped, interacting Bose-condensed gases. We investigate Josephson oscillations between interacting Bose-Einstein condensates confined in a finite size double-well trap and the non-trivial time evolution of a coherent state placed at the center of a two dimensional optical lattice. For the Josephson oscillations three time scales appear. We find that Josephson junction can sustain multiple undamped oscillations up to a characteristic time scale t_c without exciting atoms out of the condensates. Beyond the characteristic time scale t_c the dynamics of the junction are governed by fast, non-condensed particles assisted Josephson tunnelling as well as the collisions between non-condensed particles. In the non-condensed particles dominated regime we observe strong damping of the oscillations due to inelastic collisions, equilibrating the system leading to an effective loss of details of the initial conditions. In addition, we predict that an initially self-trapped BEC state will be destroyed by these fast dynamics. The time evolution of a coherent state released at the center of a two dimensional optical lattice shows a ballistic expansion with a decreasing expansion velocity for increasing two-body interactions strength and particle number. Additionally, we predict that if the two-body interactions strength exceeds a certain value, a forerunner splits up from the expanding coherent state. We also observe that this system, which is prepared far from equilibrium, can evolve to a quasistationary non-equilibrium state.