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Chinese Physics Letters

Ground State Properties for Bose-Condensed Gas in Anisotropic Traps

Xu Zhi-Jun, Haibin Li, Xin Xiao-Tian, Li Zhen, Dongmei Wang

Published May 30, 2006• 2 citations
Publisher

Abstract

Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.

DOI
10.1088/0256-307x/23/6/010

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Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross–Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 (1996) 2477] This new method is simple compared to other methods used to solve numerically the Gross–Pitaevskii equation, and one can obtain analytic and reliable results.
Based on the Gross-Pitaevskii(G-P) energy functional and variational method, we present a new method to find the ground state wave function for Bose-condensed gas in a harmonic trap at zero temperature. With this method we are able to find the analytic expression of ground state wave function and explore the relevant quantities, such as energy, chemical potential and so on. These results agree well with previous ground state numerical solutions of the G-P equation given by Dalfovo et al. Under the large number of particles N limit for repulsive interaction, our results and Thomas-Fermi approximation model approach to reaching unanimity. This new method is simple compared to other methods used to solve numerically the G-P equation, and one can obtained the analytic and reliable results.
For a Bose-condensed gas in an axially symmetric harmonic trap at zero temperature, a new trial wave function of the ground and single vortex states is considered based on the mean-field energy functional and variational method. Once the wave function is known, we can explore the particle-number dependence of relevant quantities, such as energy, chemical potential, aspect ratio of the velocity distribution and critical angular velocity for production of vortices. These results agree well with previous numerical solutions of the G-P equation given by Dalfovo et al.
For Bose–Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose–Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large- N limit of the vortex critical angular velocity for a >0, and the critical number for condensate population approaches the point of collapse for a <0, by using approximate variational method.
We study the ground-state properties of dilute Bose gas confined to both isotropic and anisotropic traps to assess the accuracy of Gross-Pitaevskii (GP) theory. To go beyond GP approximation we use Huang-Yang theory of interatomic interaction energy for hard-sphere Bose gas and use a variational method to solve the resulting modified GP equation. We also make an analytic estimate of the corrections due to higher-order terms in the interatomic interaction energy. We find that the corrections are of the order of 1 percent. However, there is a qualitative change in the density profile due to presence of logarithimic term in the interaction energy for large N (number of atoms)