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arXiv:1811.02951 · Journal of Physics B Atomic Molecular and Optical Physics

Vortex patterns in rotating dipolar Bose–Einstein condensate mixtures with squared optical lattices

Ramavarmaraja Kishor Kumar, Lauro Tomio, Arnaldo Gammal

Published Nov 23, 2018• 14 citations
arXivHTMLPDF

Abstract

Abstract Vortex-lattice patterns with transitions from regular to other variety vortex shapes are predicted in rotating binary mixtures of dipolar Bose–Einstein condensates loaded in squared optical lattices (OLs). We focus our investigation on the experimentally accessible dipolar isotopes of dysprosium ( 162,164 Dy), erbium ( 168 Er), chromium ( 52 Cr), and rubidium ( 87 Rb), by considering the binary mixtures ( 164 Dy- 162 Dy, 168 Er- 164 Dy, 164 Dy- 52 Cr and 164 Dy- 87 Rb), which are confined in strong pancake-shaped traps and loaded in squared two-dimensional (2D) OLs, where we vary the polarization angle of the dipoles, the inter-species contact interactions and the rotation frequency. The ratio between inter- to intra-species contact interaction is used for altering the miscibility properties, with the polarization of the dipolar species used for tuning the dipole–dipole interactions to repulsive or attractive. For enough higher rotation, where the inter- to intra-species scattering length ratio is larger than one, in which a richer variety of vortex-lattice patterns are predicted, including vortex sheets and 2D rotating droplet formations. The patterns can be controlled by changing the OL parameters, as shown for the symmetric 164 Dy- 162 Dy dipolar mixture. For mixtures with stronger differences in the dipole moments, such as 164 Dy- 52 Cr and 164 Dy- 87 Rb, only half the quantum vortices and circular ones have been observed, which will depend on the dipole orientations.

DOI
10.1088/1361-6455/aaf332

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Abstract Vortex-lattice patterns with transitions from regular to other variety vortex shapes are predicted in rotating binary mixtures of dipolar Bose–Einstein condensates loaded in squared optical lattices (OLs). We focus our investigation on the experimentally accessible dipolar isotopes of dysprosium ( 162,164 Dy), erbium ( 168 Er), chromium ( 52 Cr), and rubidium ( 87 Rb), by considering the binary mixtures ( 164 Dy- 162 Dy, 168 Er- 164 Dy, 164 Dy- 52 Cr and 164 Dy- 87 Rb), which are confined in strong pancake-shaped traps and loaded in squared two-dimensional (2D) OLs, where we vary the polarization angle of the dipoles, the inter-species contact interactions and the rotation frequency. The ratio between inter- to intra-species contact interaction is used for altering the miscibility properties, with the polarization of the dipolar species used for tuning the dipole–dipole interactions to repulsive or attractive. For enough higher rotation, where the inter- to intra-species scattering length ratio is larger than one, in which a richer variety of vortex-lattice patterns are predicted, including vortex sheets and 2D rotating droplet formations. The patterns can be controlled by changing the OL parameters, as shown for the symmetric 164 Dy- 162 Dy dipolar mixture. For mixtures with stronger differences in the dipole moments, such as 164 Dy- 52 Cr and 164 Dy- 87 Rb, only half the quantum vortices and circular ones have been observed, which will depend on the dipole orientations.
We study the structure and stability of vortex lattices in two-component rotating Bose-Einstein condensates with intrinsic dipole-dipole interactions and contact interactions. To address experimentally accessible coupled systems, we consider $^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$ and $^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}$ mixtures, which feature different miscibilities. The corresponding dipole moments are ${\ensuremath{\mu}}_{\mathrm{Dy}}=10{\ensuremath{\mu}}_{\mathrm{B}}$ and ${\ensuremath{\mu}}_{\mathrm{Er}}=7{\ensuremath{\mu}}_{\mathrm{B}}$, where ${\ensuremath{\mu}}_{\mathrm{B}}$ is the Bohr magneton. For comparison we also discuss a case where one of the species is nondipolar. Under a large aspect ratio of the trap, we consider mixtures in the pancake-shaped format, which are modeled by effective two-dimensional coupled Gross-Pitaevskii equations, with a fixed polarization of the magnetic dipoles. Then, the miscibility and vortex-lattice structures are studied by varying the coefficients of the contact interactions (assuming the use of the Feshbach-resonance mechanism) and the rotation frequency. We present phase diagrams for several types of lattices in the parameter plane of the rotation frequency and the ratio of inter- and intraspecies scattering lengths. The vortex structures are found to be diverse for the more miscible $^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$ composition, with a variety of shapes, whereas for the less miscible case of $^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}$, the lattice patterns mainly feature circular or square formats.
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 investigate the formation of vortices in quasi-two-dimensional dipolar Bose-Einstein condensates (BECs) through the interplay between two-body contact and long-ranged dipole-dipole interactions (DDIs), as both interactions can be tuned from repulsive to attractive. By solving the associated Gross-Pitaevskii equation for a rotating system, our initial approach concentrates on stabilizing a collapsing condensate with attractive sss-wave two-body interactions by employing sufficiently large repulsive DDIs. Subsequently, the same procedure was applied after reversing the signs of both interactions to evaluate the sensitivity of vortex formation to such an interchange of interactions. As a reference to guide our investigation, valid for generic dipolar atomic species, we have assumed a condensate with the strong dipolar dysprosium isotope, 164Dy^{164}\mathrm{Dy}164Dy. The correlation of the results with other dipolar BEC systems was exemplified by considering rotating BECs with two other isotopes, namely 168Er^{168}\mathrm{Er}168Er and 52Cr^{52}\mathrm{Cr}52Cr. For a purely dipolar condensate (no contact interactions) under fixed rotation, we show how the number of visible vortices increases as the DDI becomes more repulsive, accomplished by tuning the orientation of the dipoles through a characteristic angle parameter.
We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52 Cr and 164 Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.
Based on the two-dimensional mean-field equations for pancake-shaped dipolar Bose-Einstein condensates in a rotating frame, for both attractive and repulsive dipole-dipole interaction (DDI) as well as arbitrary polarization direction, we study the profiles of the single vortex state and show how the critical rotational frequency changes with the sss-wave contact interaction strength, DDI strength, and polarization angle. In addition, we find numerically that at the ``magic angle'' $\ensuremath{\vartheta}=arccos(\sqrt{3}/3)$, the critical rotational frequency is almost independent of the DDI strength. By numerically solving the dipolar Gross-Pitaevskii equation at high rotation speed, we identify different patterns of vortex lattices which strongly depend on the polarization direction. As a result, we undergo a study of vortex lattice structures for the whole regime of polarization direction and find evidence that the vortex lattice orientation tends to be aligned to the dipole polarization axis for positive DDI strength and to the perpendicular direction of the dipole axis for negative DDI strength.