Calculation of Bose-Einstein condensations and characteristic features of fluctuations for systems with and without a vortex in two-component alkali atom gases

Characteristic features in phases of Bose-Einstein condensations (BEC) for systems of two-components in gas phases of Alkali-metal atoms trapped by ha rmonic potentials are discussed on the basis of numerical calculations by t he use of Gross-Pitaevskii equation. Condensations with and without vortice s are considered in order to make clear spatial distributions. The shape of spatial distribution is essentially dependent on the ratio of interaction strengths between intra-components and inter-components, We emphasize the p ossibility of coexistence of vortex-free state (where the angular momentum l is 0.) for the one component in BEC and vortex state (l(z) = 1) for anoth er component whose shape is the donut-like spatial distribution. Furthermor e; fluctuations of these states are discussed. In partiucular, we concentra te our attention to the appearance of the core modes with l(z) = 0 symmetry for the component with a vortex. In connection with the behavior of the co re modes, the contribution of the component without a vortex to the stabili ty of the above vortex is discussed on the basis of numerical calculation.