Superfluid-Insulator Transition of a Bose–Einstein Condensation in a Periodic Potential and Its Interference Pattern

Abstract

Recent experiments have succeeded in observing the superfluid-Mott insulator quantum phase transition of an alkali atomic Bose–Einstein condensate in an optical lattice potential. Motivated by this work, we studied the two-dimensional Bose gas in a periodic potential by analyzing the Gross–Pitaevskii equation. We found evidence of a superfluid-insulator transition that occurs as the potential depth of the lattice is increased. For the periodic potential, the phase of the macroscopic wave function in the ground state is localized in each potential minimum. Also, according to the resugts using the Hartree–Fock–Bogoliubov equation, an energy gap appears in the lowest excitation state. We then added a parabolic trapping potential to the periodic potential and studied how the dynamics of the wave function and its interference pattern depend on the initial ground state. For the initial ground state localized by the deep periodic potential, the wave function oscillates in the central potential minimum after removing only the trapping potential. After turning off both the trapping and periodic potentials, the wave packets with periodicity escape from the condensate.