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Journal of Physics Conference Series

Dynamics of vortex lattice formation in rotating two-component Bose–Einstein condensates

Toshiaki Kanai, Makoto Tsubota

Published Mar 1, 2018• 1 citation
Publisher

Abstract

We study the dynamics of rotating two-component Bose-Einstein condensates(BECs) toward vortex lattice formation by numerically solving the two-dimensional Gross-Pitaevskii equations.The dynamics are similar to that of single-component BEC, and the whole changes of physical quantities in two cases are qualitatively similar.However, there are some differences between two cases.First, the characteristic time toward vortex entering depends on the inter-component interaction.The time toward vortex entering becomes shorter with increasing the inter-component interaction.Second, the angular momenta exchange between two components with keeping the total angular momentum.

DOI
10.1088/1742-6596/969/1/012016

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We study the dynamics of rotating two-component Bose-Einstein condensates(BECs) toward vortex lattice formation by numerically solving the two-dimensional Gross-Pitaevskii equations.The dynamics are similar to that of single-component BEC, and the whole changes of physical quantities in two cases are qualitatively similar.However, there are some differences between two cases.First, the characteristic time toward vortex entering depends on the inter-component interaction.The time toward vortex entering becomes shorter with increasing the inter-component interaction.Second, the angular momenta exchange between two components with keeping the total angular momentum.
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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.
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.
In this paper, we study the dynamics of rotating Bose--Einstein condensates (BEC) based on the Gross--Pitaevskii equation (GPE) with an angular momentum rotation term and present an efficient and accurate algorithm for numerical simulations. We examine the conservation of the angular momentum expectation and the condensate width and analyze the dynamics of a stationary state with a shift in its center. By formulating the equation in either the two-dimensional polar coordinate system or the three-dimensional cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is time reversible, unconditionally stable, efficient, and accurate for the problem. Moreover, it conserves the position density. We also apply the numerical method to study issues such as the stability of central vortex states and the quantized vortex lattice dynamics in rotating BEC.
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.