Entanglement of bosonic modes of nonplanar molecules

Entanglement of bosonic modes of material oscillators is studied in the context of two bilinearly coupled, nonlinear oscillators. These oscillators are realizable in the vibrational-cumbending motions of C-H bonds in dihalomethanes. The bilinear coupling gives rise to invariant subspaces in the Hilbert space of the two oscillators. The dynamics of entanglement and quadrature fluctuations is studied. Two classes of initial conditions, corresponding to the case where the total energy is concentrated in one of the modes and the other wherein the modes share the total energy, in the invariant subspaces are considered. The inadequacy of the known entanglement detection criteria is established and an inseparability criterion that is applicable to the states in the invariant subspaces is provided. Possibility of generating maximally entangled states is indicated. PACS: 03.67.Bg, 03.65.Ca