  We examine the entanglement induced by an angular momentum coupling between
two harmonic systems. The Hamiltonian corresponds to that of a charged particle
in a uniform magnetic field in an anisotropic quadratic potential, or
equivalently, to that of a particle in a rotating quadratic potential. We
analyze both the vacuum and thermal entanglement, obtaining analytic
expressions for the entanglement entropy and negativity through the gaussian
state formalism. It is shown that vacuum entanglement diverges at the edges of
the dynamically stable sectors, increasing with the angular momentum and
saturating for strong fields, whereas at finite temperature, entanglement is
non-zero just within a finite field or frequency window and no longer diverges.
Moreover, the limit temperature for entanglement is finite in the whole stable
domain. The thermal behavior of the gaussian quantum discord and its difference
with the negativity is also discussed.
