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Scientific Reports

Exotic vortex lattices in a rotating binary dipolar Bose-Einstein condensate

Xiao-Fei Zhang, Lin Wen, Cai-Qing Dai, Ruifang Dong, Haifeng Jiang, Hong Chang, Shougang Zhang

Published Jan 18, 2016• 25 citations
Publisher

Abstract

In the last decade, considerable advances have been made in the investigation of dipolar quantum gases. Previous theoretical investigations of a rotating binary dipolar Bose-Einstein condensate, where only one component possesses dipole moment, were mainly focused on two special orientations of the dipoles: perpendicular or parallel to the plane of motion. Here we study the ground-state and rotational properties of such a system for an arbitrary orientation of the dipoles. We demonstrate the ground-state vortex structures depend strongly on the relative strength between dipolar and contact interactions and the rotation frequency, as well as on the orientation of the dipoles. In the absence of rotation, the tunable dipolar interaction can be used to induce the squeezing or expansion of the cloud, and to derive the phase transition between phase coexistence and separation. Under finite rotation, the system is found to exhibit exotic ground-state vortex configurations, such as kernel-shell, vortex necklace, and compensating stripe vortex structures. We also check the validity of the Feynman relation, and find no significant deviations from it. The obtained results open up alternate ways for the quantum control of dipolar quantum gases.

DOI
10.1038/srep19380

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In the last decade, considerable advances have been made in the investigation of dipolar quantum gases. Previous theoretical investigations of a rotating binary dipolar Bose-Einstein condensate, where only one component possesses dipole moment, were mainly focused on two special orientations of the dipoles: perpendicular or parallel to the plane of motion. Here we study the ground-state and rotational properties of such a system for an arbitrary orientation of the dipoles. We demonstrate the ground-state vortex structures depend strongly on the relative strength between dipolar and contact interactions and the rotation frequency, as well as on the orientation of the dipoles. In the absence of rotation, the tunable dipolar interaction can be used to induce the squeezing or expansion of the cloud, and to derive the phase transition between phase coexistence and separation. Under finite rotation, the system is found to exhibit exotic ground-state vortex configurations, such as kernel-shell, vortex necklace, and compensating stripe vortex structures. We also check the validity of the Feynman relation, and find no significant deviations from it. The obtained results open up alternate ways for the quantum control of dipolar quantum gases.
Dipolar Bosonic atoms confined in external potentials open up new avenues for quantum-state manipulation and will contribute to the design and exploration of novel functional materials. Here we investigate the ground-state and rotational properties of a rotating two-component dipolar Bose-Einstein condensate, which consists of both dipolar bosonic atoms with magnetic dipole moments aligned vertically to the condensate and one without dipole moments, confined in concentrically coupled annular traps. For the nonrotational case, it is found that the tunable dipolar interaction can be used to control the location of each component between the inner and outer rings, and to induce the desired ground-state phase. Under finite rotation, it is shown that there exists a critical value of rotational frequency for the nondipolar case, above which vortex state can form at the trap center, and the related vortex structures depend strongly on the rotational frequency. For the dipolar case, it is found that various ground-state phases and the related vortex structures, such as polygonal vortex clusters and vortex necklaces, can be obtained via a proper choice of the dipolar interaction and rotational frequency. Finally, we also study and discuss the formation process of such vortex structures.
We study a harmonically trapped highly oblate two-component Bose-Einstein condensate, which consists of both dipolar and scalar bosonic atoms. When the dipoles are polarized along the symmetry axis of the trap, the dipolar atoms' density exhibits a flat-disk regime at the trap center. It is found that the dipolar component is easier to induce the first vortex when the trap is rotating about the symmetry axis, if the long-range dipolar interactions dominate over the contact interactions, and vice versa. Vortex lattices with the compensating triangular, square, and stripe structures can be formed respectively under rapid rotation. When the dipoles are polarized perpendicular to the rotation axis, the two components are generically phase separated into a kernel-shell structure due to the anisotropic dipole-dipole interactions. While the giant-hole states are induced under slow rotation, the compensating stripe vortex structures are stabilized under fast rotation. In particular, a stripe-splitting structure is found to be competing with the stripe ones. These features are expected to be observed in the mixture of 52Cr{}^{52}\mathrm{Cr}52Cr atoms in the two different spin states.
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.
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 ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions.
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.