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理论物理通讯：英文版

SO（3,2）Structure and Distributions of Two—Component Bose—Einstein Condenstates with Lower Excitations

ZHANGHong-Biao

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The eigenstates describing two-component BOse-Einstein condensates(BEC) with weakly excitations have been found,by using the SO(3,2) algebraic mean-field approximation.We show that the two-component modified BEC(see Eq(26)) possesses uniquely super-Poissonian Distribution in a fixed magnetic field along z direction.The distribution will be uncertain,if B=0.

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The eigenstates describing two-component BOse-Einstein condensates(BEC) with weakly excitations have been found,by using the SO(3,2) algebraic mean-field approximation.We show that the two-component modified BEC(see Eq(26)) possesses uniquely super-Poissonian Distribution in a fixed magnetic field along z direction.The distribution will be uncertain,if B=0.
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The ground state solutions of two-component Bose-Einstein condensates (BECs) in Bessel optical lattices (BLs) are studied by means of the balance condition between BLs strength and inter-atomic interactions. We consider a quasi-two-dimensional (2D) BECs system，strongly confined in longitudinal direction and weakly trapped in the radial direction in the transverse plane，which obeys 2D Gross-Pitaevskii equation (GPE) derived from its 3D counterpart. Analytically we obtained the atom number distribution，atom number and energy of ground state and give the parameter ranges. Compared to single-component BEC，two-component BECs exhibit a rich variety of ground state structures. These structures depend upon various parameters，in particular the inter-atomic interactions and the BLs strength. Neglecting the inter-component atomic interaction，the corresponding results of single-component situation are given.
We discuss the mean-field theories obtained from the leading order in a large-NNN approximation for one- and two-component dilute Bose gases. For a one-component Bose gas, this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature Tc{T}_{c}Tc​ is not shifted from the noninteracting gas value T0{T}_{0}T0​. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intraspecies interactions and focus on the stability of the mixture state above Tc{T}_{c}Tc​. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the interspecies interaction strength to the intraspecies interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.
The vortex structure in a space-homogeneous Bose-Einstein condensate of two particle species with different masses has been studied. It is shown that the vortex structure in the two-component condensate is described by three dimensionless parameters, which define the system. That is different from the usual one-component condensate, where the vortex is described by a parameter-less dimensionless equation with a fixed structure. A few types of vortices with different qualitative structure are explored. In particular, it is shown, that the vortex structure strongly depends on the sign of “interaction” constant of the components. There can exist the super-density vortices, when the “interaction” constant is positive. These vortices have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We show that there can exist the vortices with opposite direction of the condensate rotation near the axis and far off the axis.