Quantum dynamics of a Bose gas in finite n-well potentials in one dimension

The system under study consists of an interacting ultracold Bose gas confined by a finite n-well potential in one dimension (n = 2, 3 and 4). By numerically solving the time-dependent Schroedinger equation for the effective Hamiltonian that describes the gas confined in each potential, we determine the mean population of particles in each well as a function of time. From this analysis, we obtain a continuous transition from a coherent state to a self-trapped state as a function of the parameter Λ ∼ Ng, which takes into account the number of particles N and the interaction strength g in each system. Three different behaviours as a function of Λ are found: a coherent oscillation regime, a partial-trapped state and a self-trapped state. The partial trapping regime appears to be a novel phase for finite potentials in one dimension. A systematic quantitative study allows us to conclude that the relaxation time observed in the coherent oscillation regime for a two-well potential scales as N1/2. Finally, a comparison with an experimental realization of a Bose-Einstein condensate in a two-well potential (Albiez et al 2005 Phys. Rev. Lett. 95 010402) is presented, exhibiting good agreement.