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

Tao Yang, Andrew Henning, Keith Benedict

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5 Citations (Scopus)

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 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 of 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 a 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⊥/as the junction between the 1D and 3D crossover is not perfect.
Original languageEnglish
Article number035302
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Volume47
Issue number3
DOIs
Publication statusPublished - 21 Jan 2014
Externally publishedYes

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condensates
excitation
crossovers
traps
gases
atoms
energy

Cite this

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title = "Bogoliubov excitation spectrum of an elongated condensate throughout a transition from quasi-one-dimensional to three-dimensional",
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 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 of 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 a 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⊥/as the junction between the 1D and 3D crossover is not perfect.",
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T1 - Bogoliubov excitation spectrum of an elongated condensate throughout a transition from quasi-one-dimensional to three-dimensional

AU - Yang, Tao

AU - Henning, Andrew

AU - Benedict, Keith

PY - 2014/1/21

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N2 - 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 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 of 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 a 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⊥/as the junction between the 1D and 3D crossover is not perfect.

AB - 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 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 of 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 a 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⊥/as the junction between the 1D and 3D crossover is not perfect.

U2 - 10.1088/0953-4075/47/3/035302

DO - 10.1088/0953-4075/47/3/035302

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JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

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