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Modern Physics Letters B

Anisotropic properties of phase separation in two-component dipolar Bose–Einstein condensates

Wei Wang, Jinbin Li

Published Mar 13, 2018• 1 citation
Publisher

Abstract

Using Crank–Nicolson method, we calculate ground state wave functions of two-component dipolar Bose–Einstein condensates (BECs) and show that, due to dipole–dipole interaction (DDI), the condensate mixture displays anisotropic phase separation. The effects of DDI, inter-component s-wave scattering, strength of trap potential and particle numbers on the density profiles are investigated. Three types of two-component profiles are present, first cigar, along z-axis and concentric torus, second pancake (or blood cell), in xy-plane, and two non-uniform ellipsoid, separated by the pancake and third two dumbbell shapes.

DOI
10.1142/s0217984918500215

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Using Crank–Nicolson method, we calculate ground state wave functions of two-component dipolar Bose–Einstein condensates (BECs) and show that, due to dipole–dipole interaction (DDI), the condensate mixture displays anisotropic phase separation. The effects of DDI, inter-component s-wave scattering, strength of trap potential and particle numbers on the density profiles are investigated. Three types of two-component profiles are present, first cigar, along z-axis and concentric torus, second pancake (or blood cell), in xy-plane, and two non-uniform ellipsoid, separated by the pancake and third two dumbbell shapes.
We are pointing out relevant anisotropic effects, related to spatial separation and miscibility, due to dipole-dipole interactions in rotating binary dipolar Bose-Einstein condensates by considering symmetric ($^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$) and asymmetric ($^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}, ^{164}\mathrm{Dy}\ensuremath{-}^{87}\mathrm{Rb}$) dipolar mixtures. The binary mixtures are kept in a strong pancake-shaped trap, with repulsive two-body interactions and fixed rotation, modeled by an effective two-dimensional coupled Gross-Pitaevskii equation. The anisotropy of the dipolar interactions on miscibility and vortex-lattice structures is studied by tuning the dipole-dipole interaction (DDI) from repulsive to attractive by varying the dipole polarization angle. A clear spatial separation is verified in the densities for attractive DDI, when the inter- to intraspecies contact interaction ratio is larger than 1, being angular for symmetric mixtures and radial for asymmetric ones. The signature of hidden vortices is evidenced in the particular dipolar-symmetric case. Another relevant outcome is the observed mass-imbalance sensibility verified by the vortex-pattern binary distributions in symmetric and asymmetric-dipolar mixtures, which requires the use of a relation for nonhomogeneous mixtures to estimate the miscibility of two components.
By considering symmetric- and asymmetric-dipolar coupled mixtures (with dysprosium and erbium isotopes), we report a study on relevant anisotropic effects, related to spatial separation and miscibility, due to dipole-dipole interactions (DDIs) in rotating binary dipolar Bose-Einstein condensates. The binary mixtures are kept in strong pancake-like traps, with repulsive two-body interactions modeled by an effective two-dimensional (2D) coupled Gross-Pitaevskii equation. The DDI are tuned from repulsive to attractive by varying the dipole polarization angle. A clear spatial separation is verified in the densities for attractive DDIs, being angular for symmetric mixtures and radial for asymmetric ones. Also relevant is the mass-imbalance sensibility observed by the vortex-patterns in symmetric- and asymmetric-dipolar mixtures. In an extension of this study, here we show how the rotational properties and spatial separation of these dipolar mixture are affected by a quartic term added to the harmonic trap of one of the components.
We perform a full three-dimensional study on miscible-immiscible conditions for coupled dipolar and non-dipolar Bose–Einstein condensates (BEC), confined in anisotropic traps. In view of recent experimental studies, our focus was the atomic erbium–dysprosium ( 168 Er– 164 Dy) and dysprosium–dysprosium ( 164 Dy– 162 Dy) mixtures. The miscibility is quantified by the overlap of the two-component densities, using an appropriate defined parameter. By verifying that stable regimes for pure-dipolar coupled BECs are only possible in pancake-type traps, we obtain some non-trivial local minimum biconcave-shaped states with density oscillations in both components. For non-dipolar systems with repulsive interactions, we show that immiscible stable configurations are also possible in cigar-type geometries. The main role of the trap aspect ratio and inter-species contact interaction for the miscibility is verified for different configurations, from non-dipolar to pure dipolar systems.
This paper analyzes the properties of the two-component Bose–Einstein condensates (BECs) with long-range monopolar interaction by means of Thomas–Fermi approximation (TFA). The effects of long-range monopolar interaction, inter-component short-range s-wave scattering, and particle numbers on the density profiles and phase separation of BECs are investigated. It is shown that atoms with the small intra-component s-wave scattering length are squeezed out when the monopolar interaction of these atoms is not large enough, and the density profile will be compressed when corresponding monopolar interaction is increased. Effective zero interaction point that the s-wave scattering repulsive interaction is neutralized by monopolar attractive interaction, is found. Varying of particle numbers will cause the transformation between phase separation and faint phase separation (or mixture).
We have investigated the interference of the dipolar Bose–Einstein condensates (DBECs) released from a double-well potential and studied the effects of dipole–dipole interaction (DDI) on the interference phenomena. We find that the DDI plays an important role in the interference process. When the effective polarization direction of the dipolar atoms is in the normal direction of the condensate plane, with the increasing of the strength of DDI, the visibility of fringes reduces and the width of fringes becomes larger. When the strength of DDI is fixed and the effective polarization direction of the dipolar atoms deviates from the normal direction of the condensate plane, the interference fringes become bent. Especially, for the situation of polarization parallel to the condensate plane, the interference fringes in the central regions become wave-shaped and vortex–antivortex pairs can be formed due to the anisotropic DDI. In addition, vortex–antivortex pairs could also be created by the spatial and temporal control of the DDI.