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arXiv:1311.2087

Dark soliton in quasi-one-dimensional Bose-Einstein condensates with a Gaussian trap

Hugo L. C. Couto, Wesley Bueno Cardoso

Published Nov 8, 2013• 0 citations
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Abstract

In this paper we study dark solitons in quasi-one-dimensional Bose-Einstein condensates (BECs) in presence of an anharmonic external potential. The theoretical model is based on the Muñoz-Mateo and Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since MMD equation presents a nonpolynomial form, the soliton-sound recombination cannot display the same pattern presented in the cubic model. We perform numerical simulations to compare both cases.

DOI
10.48550/arxiv.1311.2087

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In this paper we study dark solitons in quasi-one-dimensional Bose-Einstein condensates (BECs) in presence of an anharmonic external potential. The theoretical model is based on the Muñoz-Mateo and Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since MMD equation presents a nonpolynomial form, the soliton-sound recombination cannot display the same pattern presented in the cubic model. We perform numerical simulations to compare both cases.
In this paper we study the effects of the transverse confinement strength on the dark solitons dynamics in quasi-one-dimensional Bose–Einstein condensates (BECs). The theoretical model is based on the Muoz-Mateo & Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since the MMD equation presents a nonpolynomial form, the soliton-sound recombination may not display the same pattern presented in the cubic model. We perform numerical simulations for harmonic and anharmonic (Gaussian) external potentials to compare both cases. All results via the MMD equation are in perfect agreement with the 3D simulations. Also, we noticed some differences between MMD and cubic models and changes in the soliton lifetime due to the values of the transverse confinement.
The Gross-Pitaevskii equation for a Bose-Einstein condensate confined in an elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of the condensate density and its radial velocity are approximated by Gaussian functions with real and imaginary exponents, respectively, with parameters depending on the axial coordinate and time. The effective one-dimensional system is applied to a description of the ground state of the condensate, to dark and bright solitons, to the sound and radial compression waves propagating in a dense condensate, and to weakly nonlinear waves in repulsive condensate. In the low-density limit our results reproduce the known formulas. In the high-density case our description of solitons goes beyond the standard approach based on the nonlinear Schr\"odinger equation. The dispersion relations for the sound and radial compression waves are obtained in a wide region of values of the condensate density. The Korteweg--de Vries equation for weakly nonlinear waves is derived and the existence of bright solitons on a constant background is predicted for a dense enough condensate with a repulsive interaction between the atoms.
In this paper we present mathematical analysis of one-dimensional effective models proposed in [\cite{MunozDelgado}] concerning Bose-Einstein condensates in the presence of harmonic confinement. Among the demonstrated properties, we can mention: existence, uniqueness, orbital stability, symmetry and gaussian asymptotic decay of ground-state solutions in the repulsive case. We also report formulæ for the minimal energy $E_{\mn}$ and the associate chemical potential μμμ as functions of a parameter λλλ, which is related to NNN (the number of atoms) and/or aaa (the s-wave scattering length). By considering Taylor's development of the non-quadratic therm of the energy and using appropriate gaussian functions as approximations for the ground state, we present some numerical experiments to illustrate our results.
In this paper we present a mathematical analysis of one-dimensional effective model proposed by A.M.~Mateo and V.~Delgado concerning Bose-Einstein condensates in the presence of harmonic confinement. Among the properties presented, we mention: existence, ``uniqueness'', orbital stability, symmetry and gaussian asymptotic decay of ground-state solutions in the repulsive case. We also report formul\ae\ for the minimal energy $E_{\mn}$ and the associate chemical potential μ\muμ as functions of λ\lambdaλ, which is a parameter related to NNN (the number of atoms) and/or aaa (the s-wave scattering length). By considering Taylor's development of the non-quadratic therm of the energy and using appropriate gaussian functions as approximations for the ground state, we present some numerical experiments to illustrate our results
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.
Abstract We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose–Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to a 1D OL trap can have both repulsive and attractive contact interactions. Dark-in-bright solitons are the excited states of bright solitons. The solitons, when subjected to a small perturbation, exhibit sustained breathing oscillation. Dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi-elastic. Results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross–Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.