  The fundamental quantum dynamics of two interacting oscillator systems are
studied in two different scenarios. In one case, both oscillators are assumed
to be linear, whereas in the second case, one oscillator is linear and the
other is a non-linear, angular-momentum oscillator; the second case is, of
course, more complex in terms of energy transfer and dynamics. These two
scenarios have been the subject of much interest over the years, especially in
developing an understanding of modern concepts in quantum optics and quantum
electronics. In this work, however, these two scenarios are utilized to
consider and discuss the salient features of quantum behaviors resulting from
the interactive nature of the two oscillators, i.e., coherence, entanglement,
spontaneous emission, etc., and to apply a measure of entanglement in analyzing
the nature of the interacting systems. ... For the coupled linear and
angular-momentum oscillator system in the fully quantum-mechanical description,
we consider special examples of two, three, four-level angular momentum
systems, demonstrating the explicit appearances of entanglement. We also show
that this entanglement persists even as the coupled angular momentum oscillator
is taken to the limit of a large number of levels, a limit which would go over
to the classical picture for an uncoupled angular momentum oscillator.
