Raise and fall of a bright soliton in an optical lattice

TL;DR

This paper investigates the formation, stability, and dynamics of quantum solitons in an attractive ultracold atomic gas within a one-dimensional optical lattice, revealing a transition from integrable to non-integrable behavior.

Contribution

It uncovers the quantum soliton band structure and demonstrates how solitonic states are protected from perturbations, highlighting a crossover from integrable to non-integrable dynamics.

Findings

Quantum soliton band exists for attractive interactions.

Solitonic states are robust against spatial perturbations.

System exhibits a transition from integrable to non-integrable dynamics.

Abstract

We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to $N$-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value for the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable non-ergodic to non-integrable ergodic dynamics, through non-integrable non-ergodic regimes.