The Effective Potential And Metastable State Between Two Weakly-coupled Bose-Einstein Condensates In A Double-well Potential

With temperature decreasing, ultracold atom's wave character and its tunneling ability are increased. For controlling the state of BEC in a double-well, it is very important to master the tunneling rule of Bose-Einstein condensates in trapping potential. Meanwhile the phenomenon of the macroscopic quantum tunneling is also a decay process of metastable state. We also investigate the effective potential of the system in phase space ,which is consisted of two weakly-coupled BECs through a double-well.Firstly, based on the time-dependent GP equation , we use the two-mode variational ansatz to obtain the BJJ equation when ignoring some high-order terms. Then the pseudo-spin method is introduced to obtain the effective quantized Hamiltonian of the system and a multi-particle question is transformed into a point-particle question with the constant effective mass moving under the effective potential. Finally, we numerically analyze the effective potential and get the result: in order to get higher tunneling rate in phase space, it needs to adjust the system's position energy in a symmetric double-well and the degree of asymmetry in a asymmetric double-well.