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arXiv:1406.1401 · Laser Physics

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose–Einstein condensate with repulsive short-range interactions

Emerson Chiquillo

Published Jun 18, 2014• 5 citations
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Abstract

We study the formation and dynamics of bright solitons in a quasi-one-dimensional reduced mean-field Gross-Pitaevskii equation of a dipolar Bose-Einstein condensate with repulsive short-range interactions. The study is carried out using a variational approximation and a numerical solution. Plots of chemical potential and root mean square (rms) size of solitons are obtained for the quasi-one-dimensional model of three different dipolar condensates of 52Cr, 168Er and 164Dy atoms. The results achieved are in good agreement with those produced by the full three-dimensional mean-field model of the condensate. We also study the dynamics of the collision of a train of two solitons in the quasi-one-dimensional model of every condensate above. At small velocities (zero or close to zero) the dynamics is attractive for a phase difference δ = 0, the solitons coalesce and these oscillate forming a bound soliton molecule. For a phase difference δ = π the effect is repulsive. At large velocities the collision is independent of the initial phase difference δ. This is quasi-elastic and the result is two quasi-solitons.

DOI
10.1088/1054-660x/24/8/085502

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We study the formation and dynamics of bright solitons in a quasi-one-dimensional reduced mean-field Gross-Pitaevskii equation of a dipolar Bose-Einstein condensate with repulsive short-range interactions. The study is carried out using a variational approximation and a numerical solution. Plots of chemical potential and root mean square (rms) size of solitons are obtained for the quasi-one-dimensional model of three different dipolar condensates of 52Cr, 168Er and 164Dy atoms. The results achieved are in good agreement with those produced by the full three-dimensional mean-field model of the condensate. We also study the dynamics of the collision of a train of two solitons in the quasi-one-dimensional model of every condensate above. At small velocities (zero or close to zero) the dynamics is attractive for a phase difference δ = 0, the solitons coalesce and these oscillate forming a bound soliton molecule. For a phase difference δ = π the effect is repulsive. At large velocities the collision is independent of the initial phase difference δ. This is quasi-elastic and the result is two quasi-solitons.
By numerical and variational analysis of the three-dimensional Gross–Pitaevskii equation, we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose–Einstein condensate for large repulsive atomic interactions. A phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons. At large velocities the frontal collision is elastic and the two three-dimensional solitons pass through each other undeformed. Two solitons placed side by side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction. Movie clips illustrating collision and molecule-formation dynamics of two bright and vortex-bright solitons are included.
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.
We study the statics and dynamics of a binary dipolar Bose–Einstein condensate soliton for repulsive inter and intraspecies contact interactions with the two components subject to different spatial symmetries—distinct quasi-one-dimensional and quasi-two-dimensional shapes—using numerical solution and variational approximation of a three-dimensional mean-field model. The results are illustrated with realistic values of parameters in the binary 164 Dy- 168 Er mixture. The possibility of forming robust dipolar solitons of a very large number of atoms make them of great experimental interest. The existence of the solitons is illustrated in terms of stability phase diagrams. Exotic shapes of these solitons are illustrated in isodensity plots. The variational results for statics (size and chemical potential) and dynamics (small oscillation) of the binary soliton compare well with the numerical results. A way of preparing and studying these solitons in the laboratory is suggested.
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.
Abstract We discuss scattering between a bright soliton and a soliton dimer in coupled quasi-one-dimensional dipolar Bose–Einstein condensates. The dimer is formed by each soliton from both tubes due to the attractive inter-layer dipole–dipole interaction. The dipoles within each tube repel each other, and a stable, bright soliton is stabilized via attractive contact interactions. In general, the scattering is inelastic, transferring the kinetic energy into internal modes of both soliton dimer and single soliton. Our studies reveal rich scattering scenarios, including dimer–soliton repulsion at small initial velocities, exchange of atoms between dimer and single soliton and soliton fusion at intermediate velocities. Interestingly, for some particular initial velocities, the dimer–soliton scattering results in a state of two dimers. At large initial velocities, the scattering is elastic as expected.
We demonstrate stable, robust, bright one-dimensional dipolar Bose-Einstein-condensate (BEC) solitons, moving in a direction perpendicular to the polarization direction, formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasielastic with practically no deformation. Upon small perturbation the solitons are found to exhibit sustained breathing oscillation. The findings are illustrated by numerical simulation using the three-dimensional mean-field Gross-Pitaevskii equation and a reduced two-dimensional model in three and two spatial dimensions employing realistic interaction parameters for a dipolar 164Dy^{164}\mathrm{Dy}164Dy BEC.