Cooperative two-phonon phenomena in superconductivity

Abstract

The problem of the two-photon coherent generation of entanglement photon pairs in quantum optics has been intensively studied over the passing years. It is important to note that the two-quanta cooperative effects also play a main role in other fields of physics. One example is superconductivity, where the Cooper pairs are created due to the simultaneous two-phonon exchange between electrons. It occurs when the one-phonon exchange integral between the band electrons is smaller than that of the two-phonon exchange. This is possible in many-band superconducting materials, in which the two-phonon exchange integral arises through the virtual bands of the material. Some estimates of the two-phonon superconductivity have already been given. A more realistic model which takes into account the specificities of the many-band aspects of superconductor materials will be proposed. In two-phonon processes, a more complicated temperature dependence on the order parameter is expected. A rigorous study of this anomalous temperature dependence on the order parameter of superconductors is presented. One expects that the two-phonon exchange effects can amplify the superconductivity in a way similar to the way the thermal field amplifies the two-photon super-radiance in a microcavity.