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

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 t0, and then measuring the distance between them at a later time t1 > t0. Depending on whether the distance between solitons has increased, decreased or remained unchanged, compared to its initial value at t0, 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.

Coherent impurity transport in an attractive binary Bose–Einstein condensate

“…several individual solitons forming bound objects) and also breathers, which are single solitonic entities that can be thought of as excited states of the focussing nonlinear Schrödinger equation, which have recently been engineered experimentally with matter waves for the first time [70] using an attractive gas of 85 Rb. Soliton molecules have been studied in various guises within the context of ultracold matter, for example the realization of degeneracy with atomic species possessing significant dipole-dipole interactions has led to the prediction of novel molecular states in these systems [71][72][73]. Related to this are the realisation of 'droplets' of both dipolar matter [74][75][76] and intriguingly, also light with a non-trivial angular momentum structure [77], as well as the prediction of soliton molecules in systems with nonlocal interactions [78].…”

Normal mode oscillations of a nonlocal composite matter wave soliton

“…The response function for a dipolar BEC, confined to quasi-1D trap, was derived in [39]. For three-soliton bound states we can employ the variational approach similar to that developed in [28,29]. As a suitable trial function we use the second Gauss-Hermite function where the variational parameters A(t), a(t), b(t), φ(t) have the meaning of amplitude, width, chirp and phase, respectively.…”

Soliton Dimer-soliton scattering in coupled Quasi-one-dimensional Dipolar Bose-Einstein Condensates

“…In condensates, strictly speaking, we do not deal with solitons but solitary waves due to both the external confinement and their quasi-onedimensional (Q1D) nature and thus can experience in-elastic collisions [15]. The collisional dynamics between bright solitons is studied in condensates with both contact interactions [6,13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28] and dipoledipole interactions (DDIs) [29,[31][32][33][34][35][36][37][38][39][40], which have been exploited to generate entangled soliton pairs [17,18] and design interferometers [19,22,28,41,42]. Contrary to the short-range condensates, in dipolar BECs, the long range and anisotropic nature of DDI lead to novel scenarios such as the multi-dimensional solitons [43][44][45][46][47][48] and interlayer effects [49][50][51][52]…”

“…Contrary to the short-range condensates, in dipolar BECs, the long range and anisotropic nature of DDI lead to novel scenarios such as the multi-dimensional solitons [43][44][45][46][47][48] and interlayer effects [49][50][51][52][53][54]. The latter include the stabilization of soliton complexes such as molecules or dimers, crystals and filaments [32,52,55,56].…”