Scattering of a two-soliton molecule by Gaussian potentials in dipolar Bose–Einstein condensates

Abstract

Two bright solitons in a dipolar Bose-Einstein condensate (BEC) can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two-soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Collisions of soliton molecules with single solitons are investigated, the latter playing the role of a localized defect. Due to the long-range character of dipolar forces solitons interact with each other even though their waveforms do not appreciably overlap. This is an essentially different feature of dipolar solitons compared to their counterparts in BECs with contact atomic interactions. The result of scattering significantly depends on the potential's strength and velocity of collision. For weak potentials and/or low velocity the molecule preserves its coherence, meantime the internal modes are excited. Scattering by strong potentials at moderately high velocity ends up with dissociation of the molecule. The theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). Predictions of the mathematical model are compared with numerical simulations of the nonlocal GPE, and good qualitative agreement between them is demonstrated.

Soliton Molecules with Two Frequencies

“…In their temporal versions, they appear in nonlinear optical fibers governed by the generalized nonlinear Schrödinger equation (NSE) [14], the dissipatively perturbed NSE [15], coupled NSEs describing twin-core fibers [16], or the complex Ginzburg-Landau equation [17]. There are also numerous realizations of further soliton molecules [18][19][20][21][22][23][24][25][26][27].…”

Engineering bright matter-wave solitons of dipolar condensates

“…The binding of two out-of-phase dipolar bright solitons, has been studied previously by Refs. [45,46]. Unlike their in-phase counterparts, the π phase difference preserves long-lived bound states.…”

“…Solitons whose existence depends on a non-local rather that a purely local nonlinearity represent a burgeoning area of interest in many disciplines of physics [41][42][43], and dipolar condensates provide a highlytunable platform to study such solitons. The effect of varying the relative strength of the local and nonlocal interactions has revealed novel bright [44][45][46] and dark dipolar matter wave solitons [47][48][49][50] in one dimension. Two-dimensional bright solitons are also predicted to be supported by the anisotropy of the DD interaction [51][52][53][54].…”

Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates

“…Secondly, strong trapping in one or two dimensions is required to support the presence of the roton and its rich manifestations mentioned above. Thirdly, such geometries allow access to dipolar physics in lower dimensions, including one-dimensional bright solitons [26][27][28], two-dimensional bright solitons [29][30][31][32][33][34], one-dimensional dark solitons [35][36][37][38][39], vortices and vortex lattices [40][41][42][43][44][45][46][47][48][49][50][51][52], and near-integrability [53].…”