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arXiv:cond-mat/0506118 · Physical Review Letters

Vortex Lattices in Planar Bose-Einstein Condensates with Dipolar Interactions

Jian Zhang, Hui Zhai

Published Nov 10, 2005• 87 citations
arXivHTMLPDF

Abstract

In this Letter, we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates.

DOI
10.1103/physrevlett.95.200403

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In this Letter, we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates.
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.
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.
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 calculate the critical rotation frequency at which a vortex state becomes energetically favorable over the vortex-free ground state in a harmonically trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as well as the usual sss-wave contact interactions. In the Thomas-Fermi (hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with the dipoles aligned along the axis of symmetry of the trap) tend to have lower critical rotation frequencies than their purely sss-wave contact interaction counterparts. The converse is true for dipolar condensates in prolate traps. Quadrupole excitations and center of mass motion are also briefly discussed as possible competing mechanisms to a vortex as means by which superfluids with partially attractive interactions might carry angular momentum.
Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.
We consider a rapidly rotating two-component Bose-Einstein condensate with short-range sss-wave interactions as well as dipolar coupling. We calculate the phase diagram of vortex lattice structures as a function of the intercomponent sss-wave interaction and the strength of the dipolar interaction. We find that the long-range interactions cause new vortex lattice structures to be stable and lead to a richer phase diagram. Our results reduce to the previously found lattice structures for short-range interactions and single-component dipolar gases in the corresponding limits.