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Physica Scripta

Equilibrium and scattering properties of a nonlocal three-soliton molecule in Bose–Einstein condensates with competing nonlinearities

Khelifa Mohammed Elhadj, Abdelâali Boudjemâa

Published Nov 26, 2020• 0 citations
Publisher

Abstract

Abstract We carry out numerical and variational investigation of equilibrium and scattering properties of a bright three-soliton molecule in Bose–Einstein condensates with competing local and nonlocal nonlinearities in one-dimensional geometry. Our model predicts that the degree of the nonlocality and the soliton phase may strongly affect the binding energy and the soliton width. We show that the interaction of three solitons depends on their separation distance and on their relative phase. The scattering properties of these composite nonlinear structures by Gaussian potential barrier are analyzed variationally and numerically. It is found that stable transmission and reflection where the molecular structure is preserved can occur only for a specific barrier height and soliton velocity.

DOI
10.1088/1402-4896/abce35

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Abstract We carry out numerical and variational investigation of equilibrium and scattering properties of a bright three-soliton molecule in Bose–Einstein condensates with competing local and nonlocal nonlinearities in one-dimensional geometry. Our model predicts that the degree of the nonlocality and the soliton phase may strongly affect the binding energy and the soliton width. We show that the interaction of three solitons depends on their separation distance and on their relative phase. The scattering properties of these composite nonlinear structures by Gaussian potential barrier are analyzed variationally and numerically. It is found that stable transmission and reflection where the molecular structure is preserved can occur only for a specific barrier height and soliton velocity.
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Two anti-phase bright solitons in a dipolar Bose-Einstein condensate 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. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.
Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states, known as soliton molecules. In this paper we study the scattering of a twosoliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.
The existence of stable bound states of three solitons in a Bose-Einstein condensate with nonlocal interactions is demonstrated by means of the variational approach (VA) and numerical simulations. The potential of interaction between solitons derived from VA is shown to be of molecular type, i.e., attractive at long distances and repulsive at short distances. Normal modes of a three-soliton molecule are investigated by computing small amplitude oscillations of individual solitons near their equilibrium positions. Symmetric and asymmetric stretched states of the molecule are prepared and used as initial conditions in numerical simulations of the nonlocal Gross-Pitaevskii equation. As opposed to usual triatomic molecules, we find that the frequency of the asymmetric mode of a three-soliton molecule is smaller than the one of the symmetric mode. Possible experimental settings for the observation of these results are briefly discussed.
Abstract Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross–Pitaevskii equation and good qualitative agreement between them is demonstrated.
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom sss-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schr\"odinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.