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

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.

17 pages, 6 figures

References in corpus (5)

• Degenerate Quantum Gases with Spin-Orbit Coupling
• Sub-Poissonian fluctuations in a 1D Bose gas: from the quantum quasi-condensate to the strongly interacting regime
• Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
• Quasi-1D Bose-Einstein condensates in the dimensional crossover regime
• Weakly interacting Bose gas in the one-dimensional limit

Cited by in corpus (7)

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• Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
• Collective oscillations of a Bose-Einstein condensate induced by a vortex ring
• Validity of Gross-Pitaevskii solutions of harmonically confined BEC gases in reduced dimensions
• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials