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Chinese Physics

Analytical method for yrast line states in the interacting two-component Bose-Einstein condensate

Bing-Hao Xie, Jing Hui

Published Jan 22, 2002• 12 citations
Publisher

Abstract

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC), omitting the difference between the two components, has been studied using an analytical method. The energy eigenstates and eigenvalues for L = 0, 1, 2, 3 are given. We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions. Except for symmetric states, there are antisymmetric states for the permutation of the two components, which cannot reduce to those in a single condensate case when the value of L is odd.

DOI
10.1088/1009-1963/11/2/303

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The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC), omitting the difference between the two components, has been studied using an analytical method. The energy eigenstates and eigenvalues for L = 0, 1, 2, 3 are given. We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions. Except for symmetric states, there are antisymmetric states for the permutation of the two components, which cannot reduce to those in a single condensate case when the value of L is odd.
The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC),omitting the difference between the two components,has been studied using an analytical method.The energy eigenstates and eigenvalues for L=0,1,2,3 are given,We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions.Except for symmetric states,there are antisymmetric states for the permutation of the two components,which cannot reduce to those in a single condensate case when the value of L is odd.
We study the energy eigenvalue problem and the yrast states for a harmonically trapped two-component weak-interacting Bose-Einstein condensate (BEC) using an analytical method. The yrast states and energy eigenvalues for L=0,1,2,3L=0,1,2,3L=0,1,2,3 are given in a special case. We illustrate the different eigenstate behaviors between even L and odd L for the two-component BEC. The odd-even effect of the yrast spectrum in the two-component BEC is also pointed out.
We study the energy eigenvalue and the yrast states for a harmonically two-component weak-interacting Bose–Einstein condensate (BEC) when the intra-species and interspecies scattering length are different. The energy shift for different energy eigenvalues related to intra- and interspecies scattering lengths is calculated with the perturbation method. The actual yrast spectrum is more complicated than that when intra-species and interspecies scattering length are equal. The degenerated features disappear and so do the perfect symmetric features.
We present an analytical study for density profiles of two-component Bose–Einstein condensates (BECs) in an isotropic trap within the miscible regime. The analytical equations for the density profiles and the conditions for three different density configurations are presented, which allow us to explore the density profile diagrams of general two-component BECs depending on broad ranges of experimental parameters. Furthermore, we show that the obtained explicit expressions of the density profiles can also be applied to study the collective modes of the two-component BECs, and the frequencies of the two-component BECs clearly characterize the density configurations.
We present a method to solve the model describing either a Bose-Einstein condensate (BEC) in a Mott-insulator state or a double-well BEC. We show that all the energy eigenvalues and eigenstates for an arbitrary (small or large) total atom number N can be explicitly expressed analytically in terms of a parameter $\ensuremath{\lambda}$ whose values are determined by the roots of the polynomials of the order of at most 1+int(N/2),1+\mathrm{int}(N/2),1+int(N/2), with int(x)\mathrm{int}(x)int(x) denoting x's integer part. We also show that \ensuremath{\lambda}'s explicit analytical expressions for N< 7N<~7N< 7 can be readily obtained by a simple MATHEMATICA code. Besides, finding the roots of the polynomials of the order of at most 1+int(N/2)1+\mathrm{int}(N/2)1+int(N/2) to give explicitly all the energy eigenvalues and eigenstates greatly simplifies the corresponding calculations, particularly when the total atom number N is large.