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Condensate of spin-1 atoms frozen in a unique spatial mode may possess largeinternal degrees of freedom. The scattering amplitudes of polarized cold atomsscattered by the condensate are obtained with the method of fractionalparentage coefficients that treats the spin degrees of freedom rigorously.Channels with scattering cross sections enhanced by square of atom number ofthe condensate are found. Entanglement between the condensate and thepropagating atom can be established by the scattering. The entanglement entropyis analytically obtained for arbitrary initial states. Our results also givehint for the establishment of quantum thermal ensembles in the hyperfine space.

Hyperfine state entanglement of spinor BEC and scattering atom