  A mixture of two species of pseudospin-1/2 Bose gases exhibits interesting
interplay between spin and orbital degrees of freedom. Expectation values of
various quantities of the collective spins of the two species play crucial
roles in the Gross-Pitaevskii-like equations governing the four orbital wave
functions in which Bose-Einstein condensation occurs. Consequently, the
elementary excitations of these orbital wave functions reflect properties of
the collective spins. When the coupling between the two collective spins is
isotropic, the energy gap of the gapped orbital excitation peaks, while there
is a quantum phase transition in the ground state of the effective Hamiltonian
of the two collective spins, which have previously been found to be maximally
entangled.
