Nonclassical features in the dynamics of a new quadratic quantum model of the radiation-matter interaction in a confined space

We introduce a new solvable effective Hamiltonian model describing a two-level atom coupled to a bimodal degenerate cavity field by two-photon processes. We study the evolution of the system assuming the atom and one mode in their respective ground states and the other mode in an excited Fock state. We find that the dynamics of the system displays nonclassical behaviour exhibiting, in particular, a peculiar sensitivity to the parity of the initial number of photons. We show that this quantum effect may be exploited to generate the amplification of an initially given small difference in the mode populations also enabling the preparation of quantum superpositions of macroscopically distinct field states.