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

TL;DR

This paper investigates self-attractive Bose-Einstein condensates in optical lattices, showing how the lattice controls soliton shape and stability, with a focus on collapse thresholds and maximum atom numbers.

Contribution

It introduces a combined variational, 1D NPSE, and numerical approach to analyze solitons in attractive BECs within optical lattices, highlighting collapse behavior and stability conditions.

Findings

Ground state solitons are confined to a single or multiple lattice cells.

Collapse occurs at a critical attraction strength, decreasing with lattice depth.

Maximum atom number in stable solitons ranges from 4,000 to 8,000.

Abstract

Within the framework of the mean-field description, we investigate atomic Bose-Einstein condensates (BECs), with attraction between atoms, under the action of strong transverse confinement and periodic (optical-lattice, OL) axial potential. Using a combination of the variational approximation (VA), one-dimensional (1D) nonpolynomial Schr\"{o}dinger equation (NPSE), and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation (GPE), we show that the ground state of the condensate is a soliton belonging to the semi-infinite bandgap of the periodic potential. The soliton may be confined to a single cell of the lattice, or extend 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 the depth of the periodic potential, $V_{0}$; under typical experimental conditions, the corresponding maximum number of $^{7}$Li atoms in the soliton, $N_{\max}$, ranges between $8,000$ and $4,000$. Examples of stable multi-peaked solitons are also found in the first finite bandgap of the lattice spectrum. The respective critical value $g_{c}$ again slowly decreases with the increase of $V_{0}$, corresponding to $N_{\max }\simeq 5,000$.