Nonlinear intraband tunneling of BEC in a cubic three-dimensional lattice

TL;DR

This paper investigates the nonlinear intraband tunneling of Bose-Einstein condensates in a three-dimensional cubic optical lattice, revealing new stable states and critical parameters, with potential experimental implications.

Contribution

It extends previous 2D models to 3D, identifying new stable stationary states and a critical lattice parameter in the quantum regime.

Findings

Discovery of new stable stationary atomic distributions in 3D

Identification of a critical lattice parameter for stability

Absence of quantum collapses and revivals within experimental timescales

Abstract

The intra-band 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 [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 existence of a stable 1D distribution, where all atoms populate only one X-state, may serve as a starting point in the experimental study of the nonlinear tunneling in the 3D lattice.