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arXiv:1104.0610 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose–Einstein condensate with repulsive atomic interaction

Luis E. Young-S., Paulsamy Muruganandam, Sadhan K. Adhikari

Published Apr 27, 2011• 43 citations
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Abstract

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.

DOI
10.1088/0953-4075/44/10/101001

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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.
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.
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 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.
By solving the three-dimensional Gross–Pitaevskii equation, we generate two-dimensional axially symmetric and anisotropic dipolar Bose–Einstein condensate bright solitons for repulsive atomic interaction, stabilized by only a weak one-dimensional optical lattice (OL) aligned along and perpendicular, respectively, to the dipole polarization direction. In the former case, vortex solitons can also be created. We show that it is possible to make a stable array of small interacting axially symmetric dipolar solitons put on alternate OL sites. Further, we demonstrate the elastic nature of the collision of two such solitons.
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.
The interaction between two bright solitons in a one-dimensional dipolar Bose-Einstein condensate (BEC) is investigated, with the aim of finding the regimes where they form a stable bound state, known as the soliton molecule. To study soliton interactions in BECs 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{t}_{0}t0​ and then measuring the distance between them at a later time t1>t0{t}_{1}>{t}_{0}t1​>t0​. Depending on whether the distance between solitons has increased, decreased, or remained unchanged, compared to its initial value at t0{t}_{0}t0​, we conclude that the 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 BECs, as reflected in the good agreement between the analytical and the numerical results.