  The states generated by the two-spin generalization of the two-axis
countertwisting Hamiltonian are examined. We analyze the behavior at both short
and long timescales, by calculating various quantities such as squeezing, spin
expectation values, probability distributions, entanglement, Wigner functions,
and Bell correlations. In the limit of large spin ensembles and short
interaction times, the state can be described by a two-mode squeezed vacuum
state; for qubits, Bell state entanglement is produced. We find that the
Hamiltonian approximately produces two types of spin-EPR states, and the time
evolution produces aperiodic oscillations between them. In a similar way to the
basis invariance of Bell states and two-mode squeezed vacuum states, the Fock
state correlations of spin-EPR states are basis invariant. We find that it is
possible to violate a Bell inequality with such states, although the violation
diminishes with increasing ensemble size. Effective methods to detect
entanglement are also proposed, and formulas for the optimal times to enhance
various properties are calculated.
