Title: Hyperfine state entanglement of spinor BEC and scattering atom,
Abstract: Condensate of spin-1 atoms frozen in a unique spatial mode may possess large
internal degrees of freedom. The scattering amplitudes of polarized cold atoms
scattered by the condensate are obtained with the method of fractional
parentage coefficients that treats the spin degrees of freedom rigorously.
Channels with scattering cross sections enhanced by square of atom number of
the condensate are found. Entanglement between the condensate and the
propagating atom can be established by the scattering. The entanglement entropy
is analytically obtained for arbitrary initial states. Our results also give
hint for the establishment of quantum thermal ensembles in the hyperfine space.