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 Greenʼs 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. We analyze 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, , the dynamics changes at a characteristic time, , abruptly from the slow Josephson oscillations of the BEC to fast Rabi oscillations driven by quasiparticle excitations in the trap. For times , the Josephson oscillations are undamped, in agreement with the experiments. We analyze the physical origin of the finite scale as well as its dependence on the trap parameter Δ.