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We consider a mixture of two species of spin-1 atoms with interspecies spinexchange, which may cooperate or compete with the intraspecies spin exchangesand thus dramatically affect the ground state. It represents a new class ofbosonic gases differing from single-species spinor gases. We determine theexact ground states in several parameter regimes, and study the compositestructures by using the generating function method generalized here to beapplicable to a mixture of two species of spinor gases. The most interestingphase is the so-called entangled Bose-Einstein condensation (BEC), which isfragmented BEC with quantum entanglement between the two species, and with bothinterspecies and intraspecies singlet pairs. For comparison, we also apply thegenerating function method to a mixture of two species of pseudospin-1/2 atoms,for which the total spin quantum number of each species is fixed as half of theatom number, in contrast with the case of spin-1, for which it is a variabledetermined by energetics. Consequently, singlet pairs in entangled BEC of apseudospin-1/2 mixture are all interspecies. Interspecies spin exchange leadsto novel features beyond those of spinor BEC of a single species of atoms aswell as mixtures without interspecies spin exchange.

Ground States of a Mixture of Two Species of Spinor Bose Gases with Interspecies Spin Exchange