Dynamics of an interacting Bose-Einstein condensate in a three-well potential

We study the dynamics of an ultracold interacting Bose-Einstein gas confined in a one-dimensional potential composed of three symmetrical wells. We numerically solve the time-dependent Schrödinger equation of the N-particle Hamiltonian for N = 50, 150, 500, 1000. We demonstrate that the quantum phase transition from a superfluid (SF) to a Mott insulator (MI) phase in the three-well potential depends on the strength of the interactions among the particles, the total number of particles, and the confining potential in which the particles move. We discuss the appearance of population revivals as a function of time and find that, even in the case when the interaction strength among the particles is very small, its effect has the consequence that the system never returns to the initial condition. A stationary state for long times is observed in the SF phase, while the particle population in each well remains almost equal to the initial condition in the MI phase.