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Inspired by the method that can deterministically generated the massiveentanglement through phase transitions, we study the ground state properties ofa spin-1 condensate mixture, under the premise that the heteronuclearspin-exchange collision is taken into account. We developed a effective modelto analyze the binary-coupled two-level system and studied the ground statephase transitions. Three representative quantum states with the same numberdistribution are studied and distinguished through the number fluctuations. Wedemonstrate that there will be the GreenbergerHorne-Zeilinger (GHZ) state inthe mixture if the the extra magnetic field is specifically selected oradiabatically adjusted. One advantage of preparing entangled states in mixturesis that we only need to adjust the external magnetic field, instead ofconsidering the microwaves-magnetic cooperation. Finally we estimate thefeasibility of experimentally generating the heteronuclear many-bodyentanglement in the alkali-metal atomic mixture.

Maximum Entangled State in Ultracold Spin-1 Mixture