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arXiv:1401.3184 · Physical Review A

Demixing and symmetry breaking in binary dipolar Bose-Einstein-condensate solitons

Sadhan K. Adhikari

Published Jan 31, 2014• 15 citations
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Abstract

We demonstrate a fully demixed (separated) robust and stable bright binary dipolar Bose-Einstein-condensate soliton in a quasi-one-dimensional setting formed due to dipolar interactions for repulsive contact interactions. For large repulsive interspecies contact interaction, the first species may spatially separate from the second species, thus, forming a demixed configuration, which can be spatially symmetric or symmetry broken. In the spatially symmetric case, one of the species occupies the central region, whereas, the other species separates into two equal parts and stays predominantly out of this central region. In the symmetry-broken case, the two species stay side by side. Stability phase diagrams for the binary solitons are obtained. The results are illustrated with realistic values of parameters in the binary ${}^{164}\mathrm{Dy}\text{\ensuremath{-}}{}^{168}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}\text{\ensuremath{-}}{}^{162}\mathrm{Dy}$ mixtures. The demixed solitons are really soliton molecules formed of two types of atoms. A proposal for creating dipolar solitons in experiments is also presented.

DOI
10.1103/physreva.89.013630

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We demonstrate a fully demixed (separated) robust and stable bright binary dipolar Bose-Einstein-condensate soliton in a quasi-one-dimensional setting formed due to dipolar interactions for repulsive contact interactions. For large repulsive interspecies contact interaction, the first species may spatially separate from the second species, thus, forming a demixed configuration, which can be spatially symmetric or symmetry broken. In the spatially symmetric case, one of the species occupies the central region, whereas, the other species separates into two equal parts and stays predominantly out of this central region. In the symmetry-broken case, the two species stay side by side. Stability phase diagrams for the binary solitons are obtained. The results are illustrated with realistic values of parameters in the binary 164Dy\ensuremath-168Er{}^{164}\mathrm{Dy}\text{\ensuremath{-}}{}^{168}\mathrm{Er}164Dy\ensuremath-168Er and 164Dy\ensuremath-162Dy{}^{164}\mathrm{Dy}\text{\ensuremath{-}}{}^{162}\mathrm{Dy}164Dy\ensuremath-162Dy mixtures. The demixed solitons are really soliton molecules formed of two types of atoms. A proposal for creating dipolar solitons in experiments is also presented.
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.
We demonstrate robust, stable, mobile, quasi-one-dimensional, dark-in-bright dipolar Bose-Einstein-condensate (BEC) solitons with a notch in the central plane 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. A proposal for creating dipolar dark-in-bright solitons in laboratories by phase imprinting is also discussed. A rich variety of such solitons can be formed in dipolar binary BECs, where one can have a dark-in-bright soliton coupled to a bright soliton or two coupled dark-in-bright solitons. The findings are illustrated using numerical simulation in three spatial dimensions by employing realistic interaction parameters for a dipolar 164{}^{164}164Dy BEC and a binary 164{}^{164}164Dy-162{}^{162}162Dy 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.
We study the formation of quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) symbiotic solitons bound by an interspecies dipolar interaction in a binary dipolar Bose-Einstein condensate. These binary solitons have a repulsive intraspecies contact interaction stronger than the intraspecies dipolar interaction, so that they can not be bound in isolation in the absence of an interspecies dipolar interaction. These symbiotic solitons are bound in the presence of an interspecies dipolar interaction and zero interspecies contact interaction. The quasi-1D solitons are free to move along the polarization z direction of the dipolar atoms, whereas the quasi-2D solitons move in the x-z plane. To illustrate these, we consider a ^{164}Er-^{166}Er mixture with scattering lengths a(^{164}Er)=81a_{0} and a(^{166}Er)=68a_{0} and with dipolar lengths a_{dd}(^{164}Er)≈a_{dd}(^{166}Er)≈65a_{0}, where a_{0} is the Bohr radius. In each of the two components a>a_{dd}, which stops the binding of solitons in each component in isolation, whereas a binary quasi-1D or a quasi-2D ^{164}Er-^{166}Er soliton is bound in the presence of an interspecies dipolar interaction. The stationary states were obtained by imaginary-time propagation of the underlying mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time.
We study the formation of stable bright solitons in quasi-one-dimensional (quasi-1D) spin-orbit- (SO-) and Rabi-coupled two pseudospinor dipolar Bose-Einstein condensates (BECs) of 164Dy^{164}\mathrm{Dy}164Dy atoms in the presence of repulsive contact interactions. As a result of the combined attraction-repulsion effect of both interactions and the addition of SO and Rabi couplings, two kinds of ground states in the form of self-trapped bright solitons can be formed, a plane-wave soliton (PWS) and a stripe soliton (SS). These quasi-1D solitons cannot exist in a condensate with purely repulsive contact interactions and SO and Rabi couplings (no dipole). Neglecting the repulsive contact interactions, our findings also show the possibility of creating PWSs and SSs. When the strengths of the two interactions are close to each other, the SS develops an oscillatory instability indicating a possibility of a breather solution, eventually leading to its destruction. We also obtain a phase diagram showing regions where the solution is a PWS or SS.
We study the static properties of disk-shaped binary dipolar Bose-Einstein condensates of 168{}^{168}168Er-164{}^{164}164Dy and 52{}^{52}52Cr-164{}^{164}164Dy mixtures under the action of interspecies and intraspecies contact and dipolar interactions and demonstrate the effect of dipolar interaction using the mean-field approach. Throughout this study we use realistic values of interspecis and intraspecies dipolar interactions and the intraspecies scattering lengths and consider the interspecies scattering length as a parameter. The stability of the binary mixture is illustrated through phase plots involving a number of atoms of the species. The binary system always becomes unstable as the number of atoms increases beyond a certain limit. As the interspecies scattering length increases corresponding to more repulsion, an overlapping mixed state of the two species changes to a separated demixed configuration. During the transition from a mixed to a demixed configuration as the interspecies scattering length is increased for parameters near the stability line, the binary condensate shows special transient structures in density in the form of red-blood-cell-like biconcave and Saturn-ring-like shapes, which are direct manifestations of the dipolar interaction.