Dissipative evolution of two-mode Bose-Einstein condensate in the presence of nonlinear interactions: Heisenberg operator approach

In this paper we study the qualitative dynamical evolution of atomic population imbalance and tunneling current between two Bose-Einstein condensate (BEC) interacting with each other in the presence of the intra- and inter-species collisions while the Rabi coupling between them is switched on, too. In particular, we consider the influence of dissipation process in our model to get more realized physical results. In this regard, to solve the Hamiltonian of the system, the Heisenberg operator method is used, by which the analytical solutions of the related differential equations are obtained. The population imbalance between the two BECs and the respected atomic tunneling current are then explicitly deduced for two initial state, i.e., number and coherent states in different conditions. The analytical as well as numerical results confirm the dependence of the mentioned quantities on the chosen initial state and the total number of atoms in the system which is in consistence with experimental observations. As is observed, a new kind of macroscopic quantum self-trapping (MQST) effect is also occurred in the population imbalance at certain conditions. Two distinct types of collapse-revival phenomena, depending on the relative strength of tunneling and collisional interactions, can be seen in the behavior of atomic population imbalance and tunneling current. Interestingly, collapse-revival phenomenon is disappeared in the intermediate regime and a new oscillatory step-like pattern is observed in the dynamics of the system.