  We investigate the exact dynamics of a system of two independent harmonic
oscillators coupled through their angular momentum. The exact analytic solution
of the equations of motion for the field operators is derived, and the
conditions for dynamical stability are obtained. As application, we examine the
emergence of squeezing and mode entanglement for an arbitrary separable
coherent initial state. It is shown that close to instability, the system
develops considerable entanglement, which is accompanied with simultaneous
squeezing in the coordinate of one oscillator and the momentum of the other
oscillator. In contrast, for weak coupling away from instability, the generated
entanglement is small, with weak alternating squeezing in the coordinate and
momentum of each oscillator. Approximate expressions describing these regimes
are also provided.
