## Bogoliubov excitation spectrum of an elongated condensate from quasi-one-dimensional to three-dimensional transition    [PDF]

Tao Yang, Andrew J. Henning, Keith A. Benedict
The quasiparticle excitation spectra of a Bose gas trapped in a highly anisotropic trap are studied with respect to varying total number of particles by numerically solving an effective one-dimensional (1D) Gross-Pitaevskii (GP) equation proposed by Meteo \textit{et al.} \cite{mun} recently. We get static properties and Bogoliubov spectra of the system in a large energy domain. We show that this method is computational efficient and very acute for a condensate system undergoing 1D to three-dimensional (3D) cigar-shaped phase transition by comparing our results with those calculated by the 3D-GP equation and analytical results obtained under some limiting cases. We identify the applicable parameter space for the effective 1D-GP equation and find that this equation fails to describe a system with large number of atoms. We also identify that the description of the transition from 1D BEC to 3D cigar-shaped BEC using this equation is not smooth as mentioned in Ref.\cite{mat2}, which highlight the fact that for a finite value of $a_\perp/a_s$ the junction between the 1D and 3D limiting cases is not perfect.
View original: http://arxiv.org/abs/1304.7302