  We consider the evolution of a two-mode system of bosons under the action of
a Hamiltonian that generates linear SU(2) transformations. The Hamiltonian is
generic in that it represents a host of entanglement mechanisms, which can thus
be treated in a unified way. We start by solving the quantum dynamics
analytically when the system is initially in a Fock state. We show how the two
modes get entangled by evolution to produce a coherent superposition of vortex
states in general, and a single vortex state under certain conditions. The
degree of entanglement between the modes is measured by finding the explicit
analytical dependence of the Von Neumann entropy on the system parameters. The
reduced state of each mode is analyzed by means of its correlation function and
spatial coherence function. Remarkably, our analysis is shown to be equally as
valid for a variety of initial states that can be prepared from a two-mode Fock
state via a unitary transformation and for which the results can be obtained by
mere inspection of the corresponding results for an initial Fock state. As an
example, we consider a quantum vortex as the initial state and also find
conditions for its revival and charge conjugation. While studying the evolution
of the initial vortex state, we have encountered and explained an interesting
situation in which the entropy of the system does not evolve whereas its wave
function does. Although the modal concept has been used throughout the paper,
it is important to note that the theory is equally applicable for a
two-particle system in which each particle is represented by its bosonic
creation and annihilation operators.
