Population imbalance, macroscopic tunneling and intermodal entanglement of two-mode Bose–Einstein condensate under the influence of dissipation process

Abstract

In this paper, we study the dissipative dynamics of a system which is composed of two atomic Bose–Einstein condensates (BECs) interacting through the Josephson-like coupling. To model a more realistic physical system, the inevitable dissipation effect is considered via the interaction between the system and its environment, in particular, a thermal reservoir. In this respect, after introducing a proper Hamiltonian for the model, we analytically solve the corresponding quantum Heisenberg–Langevin equations and then obtain explicit analytical expressions for population imbalance, macroscopic tunneling current and intermodal entanglement. Generally, the dynamics of the system is very sensitive to the chosen values of tunneling coupling strength, initial population as well as the characteristics of interaction between the system and its reservoirs. Also, the time evolution of the above-mentioned physical quantities shows oscillatory decaying behavior where the frequency of oscillations depends on the strength of tunneling interaction between the two subsystems. The oscillatory pattern of population imbalance and tunneling current is more regular in comparison with the intermodal entanglement. Although the system is always separable for low initial population, we show that it tends to an entangled state as its initial population is increased. In particular, the amount and the time interval of the entanglement can be effectively controlled via the dissipation parameter. Also, to get an insight into the effect of nonlinear interaction on the behavior of dynamical evolution of the considered system, we numerically investigate the population imbalance in the absence and presence of such interactions. A qualitative comparison shows that the previous theoretical works and numerical simulations confirm our obtained results.