Three-dimensional analysis of vortex-lattice formation in rotating Bose-Einstein condensates using smoothed-particle hydrodynamics

TL;DR

This paper demonstrates a 3D simulation of vortex lattice formation in rotating Bose-Einstein condensates using smoothed-particle hydrodynamics, successfully reproducing key behaviors observed experimentally and validating the numerical scheme.

Contribution

The study extends a previously developed 2D SPH scheme to 3D, accurately simulating vortex lattice formation and behaviors in rotating BECs.

Findings

Reproduced vortex lattice shapes in 3D BECs

Observed stable vortex lines along the vertical axis

Simulated vortex line bending near condensate edges

Abstract

Recently, we presented a new numerical scheme for vortex lattice formation in a rotating Bose-Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit time-integrating scheme; our SPH scheme could reproduce the vortex lattices and their formation processes in rotating quasi-two-dimensional (2D) BECs trapped in a 2D harmonic potential. In this study, we have successfully demonstrated a simulation of rotating 3D BECs trapped in a 3D harmonic potential forming "cigar-shaped" condensates. We have found that our scheme can reproduce the following typical behaviors of rotating 3D BECs observed in the literature: (i) the characteristic shape of the lattice formed in the cross-section at the origin and its formation process, (ii) the stable existence of vortex lines along the vertical axis after reaching the steady state, (iii) a "cookie-cutter" shape, with a similar lattice shape observed wherever we cut the condensate in a certain range in the vertical direction, (iv) the bending of vortex lines when approaching the inner edges of the condensate, and (v) the formation of vortex lattices by vortices entering from outside the condensate. Therefore, we further validated our scheme by simulating rotating 3D BECs.