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We consider the ground state of a mixture of two pseudospin-$\1/2$ Bose gaseswith interspecies spin exchange in a trapping potential. In the mean fieldapproach, the ground state can be described in terms of four wave functionsgoverned by a set of coupled Gross-Pitaevskii-like (GP-like) equations, whichdiffer from the usual GP equations in the existence of an interference term dueto spin-exchange coupling between the two species. Using these GP-likeequations, we calculate such ground state properties as chemical potentials,density profiles and spin density profiles, which are directly observable inexperiments. We compare the cases with and without spin exchange. It isdemonstrated that the spin exchange between the two species lowers the chemicalpotentials, tends to equalize the wave functions of the two pseudospincomponents of each species, and thus homogenizes the spin density. The novelfeatures of the density and spin density profiles can serve as experimentalprobes of this novel Bose system.

Number and spin densities in the ground state of a trapped mixture of two pseudospin-1/2 Bose gases with interspecies spin-exchange interaction