Effective Hamiltonian of an ultracold Bose gas confined in a four-well optical lattice

In this paper we study an interacting Bose gas at low temperatures, confined in a one-dimensional potential composed of four wells. In order to derive and validate the effective Hamiltonian that describes this system, we study the stationary states of a particle confined in the four-well potential. In particular, we calculate the energies and the corresponding wave functions for the ground state and for the three lowest excited states. It was established that the effective Hamiltonian of a four-well optical lattice is composed of tunneling terms among all the wells, and interaction terms between pairs of particles within the same well.