Entanglement Growing Beyond Limits

I consider two bosonic modes of a laser model proposed by F. Schwabl and myself [Ergebnisse der Exakten Naturwissenschaften 219–242 (1964)]. They describe photons and a field of atoms in an excited state. Since the latter has a negative energy the coupling between them leads to amplitudes increasing exponentially in time. This in turn leads to a linear increase of the entropy of the state restricted to one mode. Since we started from a product state, this entropy is just the entanglement of formation [Bennet et al. Phys. Rev. A. 54, 3824 (1996)].