Bogoliubov modes of a dipolar condensate in a cylindrical trap

TL;DR

This paper introduces a fast, accurate numerical method using Hankel transforms to compute Bogoliubov excitations in dipolar Bose-Einstein condensates within cylindrical traps, enabling detailed analysis of excitation modes and quantum depletion.

Contribution

A novel numerical algorithm based on Hankel transforms for direct calculation of Bogoliubov modes in dipolar condensates with cylindrical symmetry.

Findings

Successfully computed multiple excitation modes.

Analyzed mode behavior across different trap geometries.

Estimated quantum depletion using the new method.

Abstract

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.