Ultracold Bosons with 3-Body Attractive Interactions in an Optical Lattice

TL;DR

This paper investigates how an optical lattice influences the stability of solitons in one-dimensional ultracold bosons with three-body attraction, revealing a stability window induced by the lattice.

Contribution

It demonstrates that an optical lattice can stabilize solitons at the critical three-body interaction point, which is unstable without the lattice.

Findings

Optical lattice creates a stability window for solitons.

Stability depends on the lattice strength and trap alignment.

Without lattice, solitons are unstable at critical interaction.

Abstract

We study the effect of an optical lattice (OL) on the ground-state properties of one-dimensional ultracold bosons with three-body attraction and two-body repulsion, which are described by a cubic-quintic Gross-Pitaevskii equation with a periodic potential. Without the OL and with a vanishing two-body interaction term, soliton solutions of the Townes type are possible only at a critical value of the three-body interaction strength, at which an infinite degeneracy of the ground-state occurs; a repulsive two-body interaction makes such localized solutions unstable. We show that the OL opens a stability window around the critical point when the strength of the periodic potential is above a critical threshold. We also consider the effect of an external parabolic trap, studying how the stability of the solitons depends on matching between minima of the periodic potential and the minimum of the parabolic trap.