  A collective spin model is used to describe two species of mutually
interacting ultracold bosonic atoms confined to a toroidal trap. The system is
modeled by a Hamiltonian that can be split into two components, a linear part
and a quadratic part, which may be controlled independently. We show the linear
component is an analog of a Zeeman Hamiltonian, and the quadratic component
presents a macroscopic simulator for spin-orbit and hyperfine interactions. We
determine a complete set of commuting observables for both the linear and
quadratic Hamiltonians, and derive analytical expressions for their respective
spectra and density of states. We determine the conditions for generating
maximal entanglement between the two species of atoms with a view to
applications involving quantum correlations among spin degrees of freedom, such
as in the area of quantum information.
