  Spin coherent states are the matter equivalent of optical coherent states,
where a large number of two component particles form a macroscopic state
displaying quantum coherence. Here we give a detailed study of entanglement
generated between two spin-1/2 BECs due to an Sz1 Sz2 interaction. The states
that are generated show a remarkably rich structure showing fractal
characteristics. In the limit of large particle number N, the entanglement
shows a strong dependence upon whether the entangling gate times are a rational
or irrational multiple of pi/4. We discuss the robustness of various states
under decoherence and show that despite the large number of particles in a
typical BEC, entanglement on a macroscopic scale should be observable as long
as the gate times are less than hbar/J sqrt[N], where J is the effective
BEC-BEC coupling energy. Such states are anticipated to be useful for various
quantum information applications such as quantum teleportation and quantum
algorithms.
