Temporal non-equilibrium dynamics of a Bose-Josephson junction in presence of incoherent excitations

Abstract

The time-dependent non-equilibrium dynamics of a Bose-Einstein condensate (BEC) typically generates incoherent excitations out of the condensate due to the finite frequencies present in the time evolution. We present a detailed derivation of a general non-equilibrium Green's function technique that describes the coupled time evolution of an interacting BEC and its single-particle excitations in a trap, based on an expansion in terms of the exact eigenstates of the trap potential.Weanalyze the dynamics of a Bose system in a small double-well potential with initially all particles in the condensate. When the trap frequency is larger than the Josephson frequency, δ > ωJ, the dynamics changes at a characteristic time, τc, abruptly from the slow Josephson oscillations of the BEC to fast Rabi oscillations driven by quasiparticle excitations in the trap. For times t < τc, the Josephson oscillations are undamped, in agreement with the experiments. We analyze the physical origin of the finite scale τc as well as its dependence on the trap parameter δ.