Nonlinear correction to the boson Josephson-junction model

We investigate the nonlinear correction to two weakly linked Bose-Einstein condensates realized by two square wells. In the framework of the two-mode approximation, a tunneling term chi describing the nonlinear tunneling between the nonlinear effective potential is introduced. When the nonlinear interaction is weak, our mode reduces to the well-known boson Josephson-junction model [A. Smerzi et al., Phys. Rev. Lett. 79, 4950 (1997); S. Raghavan et al., Phys. Rev. A 59, 620 (1999)], while in the case of strong nonlinear interactions, our model presents one crucial correction and gives a better description of the static and dynamical properties of the system than that model.