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Yunnan Daxue xuebao. Shehui kexue ban

Triangular vortex lattices in Bose-Einstein condensates

Yun‐De Li

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The basic laws of triangular vortex lattices' formation in Bose-Einstein condensates(BEC) are discussed.A solution of triangular lattices is attained by deducing the Gross-Pitaevskii equation,which describes the behaviors of BECs trapped in magneto-optical potential.In addition,a brief explanation to the latest related experiments as well as results is also discussed.

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The basic laws of triangular vortex lattices' formation in Bose-Einstein condensates(BEC) are discussed.A solution of triangular lattices is attained by deducing the Gross-Pitaevskii equation,which describes the behaviors of BECs trapped in magneto-optical potential.In addition,a brief explanation to the latest related experiments as well as results is also discussed.
We study the vortex pinning effect in a Bose-Einstein condensate in the presence of a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. We consider a triangular lattice potential created by blue-detuned laser beams. By rotating the lattice potential, we observe a structural phase transition from the Abrikosov vortex lattice to the pinned vortex lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, strength, and lattice constant of a rotating lattice potential. Our simulation results clearly show that the lattice potential has a strong vortex pinning effect when the vortex density coincides with the density of the pinning points.
We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.
We study the vortex pinning effect on the vortex lattice structure of the rotating two-component Bose-Einstein condensates (BECs) in the presence of impurities or disorder by numerically solving the time-dependent coupled Gross-Pitaevskii equations. We investigate the transition of the vortex lattice structures by changing conditions such as angular frequency, the strength of the inter-component interaction and pinning potential, and the lattice constant of the periodic pinning potential. We show that even a single impurity pinning potential can change the unpinned vortex lattice structure from triangular to square or from triangular to a structure which is the overlap of triangular and square. In the presence of a periodic pinning potential or optical lattice, we observe the structural transition from the unpinned vortex lattice to the pinned vortex lattice structure of the optical lattice. In the presence of a random pinning potential or disorder, the vortex lattice melts following a two-step process by creation of lattice defects, dislocations, and disclinations, with the increase of rotational frequency, similar to that observed for single-component Bose-Einstein condensates. However, for the binary BECs, we show that the two-step vortex lattice melting also occurs with increasing strength of the intercomponent interaction.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.