Soliton and traveling wave solutions in coupled one-dimensional condensates

TL;DR

This paper explores soliton and traveling wave solutions in coupled one-dimensional Bose-Einstein condensates, providing analytical results and discussing experimental relevance, especially beyond the sine-Gordon model with asymmetry considerations.

Contribution

It introduces new soliton solutions in coupled 1D condensates with asymmetry, extending the sine-Gordon model and analytically calculating their energy densities.

Findings

Analytical soliton and traveling wave solutions derived.

New solutions emerge due to asymmetry between condensates.

Relevance to current experiments in ultracold atom systems.

Abstract

Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports various density and phase solitons. We explore the physics using the bosonization technique, in which the phase and density are conjugate pairs, and determine its effective Language equation and the associated equation of motion. We show that in the presence of asymmetry between the two condensates, new solutions beyond those in the sine-Gordon model emerge. We calculate the traveling wave solutions and soliton solutions in this model and determine their corresponding energy densities analytically. Finally, we discuss the relevance of these solutions to the experiments and discuss their observations. This theory does not rely on the mechanism of quasi-particle excitation, which yields the Lee-Huang-Yang correction in higher dimensions, and is thus much more suitable to describe the physics in 1D systems. Since the physical models have already been realized in experiments, this work opens a new frontier for the realization of various soliton and periodic solutions using two coupled condensates.