Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices

Abstract

Within the framework of a mean-field description, we investigate atomic Bose-Einstein condensates, with attraction between atoms, under the action of a strong transverse confinement and periodic [optical-lattice (OL)] axial potential. Using a combination of the variational approximation, one-dimensional (1D) nonpolynomial Schr\"odinger equation, and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation, we show that the ground state of the condensate is a soliton belonging to the semi-infinite band gap of the periodic potential. The soliton may be confined to a single cell of the lattice or extended to several cells, depending on the effective self-attraction strength $g$ (which is proportional to the number of atoms bound in the soliton) and depth of the potential, ${V}_{0}$, the increase of ${V}_{0}$ leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton's shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, $g={g}_{c}$, which gradually decreases with the increase of ${V}_{0}$; under typical experimental conditions, the corresponding maximum number of $^{7}\mathrm{Li}$ atoms in the soliton, ${N}_{\mathrm{max}}$, ranges between 8000 and 4000. Examples of stable multipeaked solitons are also found in the first finite band gap of the lattice spectrum. The respective critical value ${g}_{c}$ again slowly decreases with the increase of ${V}_{0}$, corresponding to ${N}_{\mathrm{max}}\ensuremath{\simeq}5000$.