Interaction of solitons in dipolar Bose-Einstein condensates and formation of soliton molecules

TL;DR

This paper investigates how bright solitons in dipolar Bose-Einstein condensates interact and form stable bound states called soliton molecules, using a variational approach and proposing an experimental method to estimate their binding energy.

Contribution

It introduces a variational method to analyze soliton interactions in dipolar BECs and proposes an experimentally feasible way to measure soliton molecule binding energy.

Findings

Good agreement between analytical and numerical results.

Identification of regimes for stable soliton molecule formation.

Method for estimating binding energy via soliton dissociation.

Abstract

The interaction between two bright solitons in a dipolar Bose-Einstein condensate (BEC) has been investigated aiming at finding the regimes when they form a stable bound state, known as soliton molecule. To study soliton interactions in BEC we employed a method similar to that used in experimental investigation of the interaction between solitons in optical fibers. The idea consists in creating two solitons at some spatial separation from each other at initial time $t_0$, and then measuring the distance between them at a later time $t_1 > t_0$. Depending on whether the distance between solitons has increased, decreased or remained unchanged, compared to its initial value at $t_0$, we conclude that soliton interaction was repulsive, attractive or neutral, respectively. We propose an experimentally viable method for estimating the binding energy of a soliton molecule, based on its dissociation at critical soliton velocity. Our theoretical analysis is based on the variational approach, which appears to be quite accurate in describing the properties of soliton molecules in dipolar BEC, as reflected in good agreement between the analytical and numerical results.