Nonlinear intraband tunneling of a Bose-Einstein condensate in a cubic three-dimensional lattice

Abstract

The intraband tunneling of a Bose-Einstein condensate between three degenerate high-symmetry $X$ points of the Brillouin zone of a cubic optical lattice is studied in the quantum regime by reduction to a three-mode model. The mean-field approximation of the deduced model is described. Compared to the previously reported two-dimensional (2D) case [V. S. Shchesnovich and V. V. Konotop, Phys. Rev. A 75, 063628 (2007)], which is reducible to the two-mode model, in the case under consideration there exist a number of new stable stationary atomic distributions between the $X$ points and a new critical lattice parameter. The quantum collapses and revivals of the atomic population dynamics are absent for the experimentally realizable time span. The 2D stationary configurations, embedded into the 3D lattice, turn out to be always unstable, while the existence of a stable 1D distribution, where all atoms populate only one $X$ state, may serve as a starting point in an experimental study of nonlinear tunneling in a 3D lattice.