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arXiv · 1304.7302

Bogoliubov excitation spectrum of an elongated condensate from quasi-one-dimensional to three-dimensional transition

Tao Yang·Andrew J. Henning·Keith A. Benedict
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Abstract

The quasiparticle excitation spectra of a Bose gas trapped in a highly anisotropic trap is studied with respect to varying total number of particles by numerically solving the effective one-dimensional (1D) Gross-Pitaevskii (GP) equation proposed recently by Mateo \textit{et al.}. We obtain the static properties and Bogoliubov spectra of the system in the high energy domain. This method is computationally efficient and highly accurate for a condensate system undergoing a 1D to three-dimensional (3D) cigar-shaped transition, as is shown through a comparison our results with both those calculated by the 3D-GP equation and analytical results obtained in 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 Bose-Einstein condensate (BEC) to 3D cigar-shaped BEC using this equation is not smooth, which highlights the fact that for a finite value of $a_\perp/a_s$ the junction between the 1D and 3D crossover is not perfect.

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Tao Yang, Andrew J. Henning, Keith A. Benedict. 2014-01-15. Bogoliubov excitation spectrum of an elongated condensate from quasi-one-dimensional to three-dimensional transition. https://doi.org/10.1088/0953-4075%2F47%2F3%2F035302

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