  We consider a mixture of two distinct species of atoms of pseudospin-1/2 with
both intraspecies and Interspecies spin-exchange interactions, and find all the
ground stats in a general case of the parameters in the effective Hamiltonian.
In general, corresponding to the two species and two pseudo-spin states, there
are four orbital wave functions into which the atoms condense. We find that in
certain parameter regimes, the ground state is the so-called polarized
entangled Bose-Einstein condensation, i.e. in addition to condensation of
interspecies singlet pairs, there are unpaired atoms with spins polarized in
the same direction. The interspecies entanglement and polarization
significantly affect the generalized Gross-Pitaevskii equations governing the
four orbital wave functions into which the atoms condense, as an interesting
interplay between spin and orbital degrees of freedom.
