Solitons in Tonks-Girardeau gas with dipolar interactions

TL;DR

This paper investigates the existence, shape, and dynamics of bright and dark solitons in a dipolar Tonks-Girardeau gas modeled by a nonlocal quintic nonlinear Schrödinger equation, revealing new soliton behaviors and interactions.

Contribution

It introduces a model for dipolar TG gas solitons using a nonlocal quintic NLSE and explores their shapes, dynamics, and collision behaviors, including comparisons with local cubic-quintic models.

Findings

Existence of flat-top and compacton-like solitons in the TG gas.

Dark-soliton pairs are generated during gas contraction under increasing dipolar attraction.

Soliton collisions often lead to merger into breathers due to strong attraction.

Abstract

The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas with dipole-dipole (DD) interactions is reported. The governing equation is taken as the quintic nonlinear Schr\"{o}dinger equation (NLSE) with the nonlocal cubic term accounting for the DD attraction. In different regions of the parameter space (the dipole moment and atom number), matter-wave solitons feature flat-top or compacton-like shapes. For the flat-top states, the NLSE with the local cubic-quintic (CQ) nonlinearity is shown to be a good approximation. Specific dynamical effects are studied assuming that the strength of the DD interactions is ramped up or drops to zero. Generation of dark-soliton pairs in the gas shrinking under the action of the intensifying DD attraction is observed. Dark solitons exhibit the particle-like collision behavior. Peculiarities of dipole solitons in the TG gas are highlighted by comparison with the NLSE including the local CQ terms. Collisions between the solitons are studied too. In many cases, the collisions result in merger of the solitons into a breather, due to strong attraction between them.