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arXiv:1801.07225 · Physical Review A

Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates

Yongyong Cai, Yongjun Yuan, Matthias Rosenkranz, Han Pu, Weizhu Bao

Published Aug 10, 2018• 22 citations
arXivHTMLPDF

Abstract

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 $s$-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.

DOI
10.1103/physreva.98.023610

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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'' \ensuremathϑ=arccos(3/3)\ensuremath{\vartheta}=arccos(\sqrt{3}/3)\ensuremathϑ=arccos(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.
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.
We investigate the vortex lattices of harmonically confined quasi-two-dimensional tilted rotational dipolar Bose-Einstein condensates. By employing an extended Gross-Pitaevskii equation for a rotating condensate, we reveal the structural transformation of vortices from square to triangular lattices as the tilt of dipolar bosons relative to the polarization axis approaches a critical angle. When the tilt of the magnetic dipoles surpasses the magic angle, the condensate elongates diagonally and becomes devoid of vortices. Moreover, we include the Lee-Huang-Yang correction, which enables the formation of vortices in the elongated condensate. Additionally, when dipoles are oriented perpendicular to the polarization axis, the Lee-Huang-Yang correction results in the fragmentation of condensates under strong rotation. The quench dynamics of the rotational frequency demonstrate the development of vortex lattices; however, with a strong rotational quench, the condensate remains free of vortices. Our numerical analysis highlights the beyond mean-field effects of the rotational properties of anisotropic dipolar bosons, which can be observed in current dipolar quantum gas experiments.
In this paper, we study the dynamics of a single vortex and a corotating vortex pair in dipolar Bose-Einstein condensates under rotation.The results are obtained by numerically solving the nonlinear Gross-Pitaevskii equation.It is displayed that the dynamics behaviour is strongly dependent on the polarization angle and the rotation frequency.For a single vortex, the clockwise rotation occurs with an increasing rotation frequency, and the rotation direction is constant.The x coordinate and y coordinate as a function of time show that the single vortex is accelerated.The oscillation frequency is larger in the case of the totally repulsive dipolar interaction than for the anisotropic dipolar interaction.For a corotating vortex pair, the dynamic is different than in the case of a single vortex.When the rotation frequency is gradually increased, the corotating vortex pair spins from anti-clockwise to clockwise direction and the anisotropic dipolar interaction is fully embodied.In this process, the system has a critical rotation frequency to accomplish such transition.In addition, the vortex motion is confined to a small extent at this critical rotation frequency.These results reflect a competition between rotation and dipolar interaction.
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.
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.
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.