Vortices in D-dimensional anisotropic Bose-Einstein condensates: dimensional perturbation theory with hypercylindrical symmetry

TL;DR

This paper develops an analytical approximation method for studying vortices in D-dimensional anisotropic Bose-Einstein condensates using dimensional perturbation theory, revealing energy level crossings and effects of trap anisotropy.

Contribution

It introduces a zeroth-order semiclassical approximation for the hypercylindrical Gross-Pitaevskii equation in arbitrary dimensions, accounting for anisotropy and vortex properties.

Findings

Derived analytical expressions for energy, density, and chemical potential in arbitrary dimensions.

Identified energy level crossings as a function of interaction strength and anisotropy.

Explored effects of trap anisotropy on effective dimensionality and vortex characteristics.

Abstract

We investigate D-dimensional atomic Bose-Einstein condensates in a hypercylindrical trap with a vortex core along the z-axis and quantized circulation $\hbar m$. We analytically approximate the hypercylindrical Gross-Pitaevskii equation using dimensional perturbation theory with perturbation parameter $\delta=1/(D+2|m|-d)$, \textcolor{black}{where $d$ controls the contribution of kinetic energy at zeroth order}. We derive the zeroth-order ($\delta \to 0$) semiclassical approximations for the condensate energy, density, chemical potential, and critical vortex rotation speed in arbitrary dimensions. We investigate the effect of trap anisotropy on lower effective dimensionality and compute properties of vortices in higher dimensions motivated by the study of synthetic dimensions and holographic duality, where a higher-dimensional gravitational model corresponds to a lower-dimensional quantum model. In the zeroth-order approximation, we observe crossings between energy levels for different dimensions as a function of interaction strength and anisotropy parameters.