Entanglement of two harmonic modes coupled by angular momentum

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.