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arXiv:cond-mat/0410148 · Physical Review A

Properties of quasi-two-dimensional condensates in highly anisotropic traps

Gerald Hechenblaikner, J. M. Krueger, Christopher J. Foot

Published Jan 20, 2005• 20 citations
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Abstract

We theoretically investigate some of the observable properties of quasi-two-dimensional condensates. Using a variational model based on a Gaussian-parabolic trial wave function we calculate chemical potential, condensate size in time-of-flight, release energy, and collective excitation spectrum for varying trap geometries and atom numbers and find good agreement with recent published experimental results.

DOI
10.1103/physreva.71.013604

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We theoretically investigate some of the observable properties of quasi-two-dimensional condensates. Using a variational model based on a Gaussian-parabolic trial wave function we calculate chemical potential, condensate size in time-of-flight, release energy, and collective excitation spectrum for varying trap geometries and atom numbers and find good agreement with recent published experimental results.
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We develop a simple analytical model based on a variational method to explain the properties of trapped cylindrically symmetric Bose-Einstein condensates of varying degrees of anisotropy, well into the regimes of effective one dimension and effective two dimensions. Our results are accurate in regimes where the Thomas-Fermi approximation breaks down and they are shown to be in agreement with recent experimental data. We also present analytic expressions for various ground-state properties and quasiparticle excitations valid for highly anisotropic condensates.
We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the sss-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.
We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low-energy pseudopotentials is proposed and justified by the agreement with results of numerical multichannel calculations. The time dependent variational method is adapted to reveal several interesting features observed in numerical solutions of condensate wave function. Collective low-energy shape oscillations and their stability inside electric fields are investigated. Our results shed new light into macroscopic coherence properties of interacting quantum degenerate atomic gases.