标题： 偶极凝聚体在圆柱形势阱中的Bogoliubov模式 显示英文标题

标题： Bogoliubov modes of a dipolar condensate in a cylindrical trap

摘要： 由于相互作用的长程性质，具有偶极相互作用的玻色-爱因斯坦凝聚体的性质计算已被证明是一个计算量大的问题，限制了应用范围。 特别是，在具有圆柱对称性的三维谐波势中，最低的博戈留波夫激发态迄今为止是通过时间依赖扰动的傅里叶分析或近似变分方法间接计算的。 我们开发了一种基于汉克尔变换的快速且精确的数值算法，用于计算圆柱对称势中偶极玻色-爱因斯坦凝聚体的性质。 作为应用，我们能够通过直接求解博戈留波夫-德根内斯方程来计算许多激发模式。 我们研究了不同势几何结构下激发模式的行为。 我们利用这些结果，通过精确模式的计算和局部密度近似的使用来计算凝聚体的量子耗尽。 显示英文摘要

摘要： 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.