Phonons in thin optically irradiated superconductors ; spectrum and possible definition of a phonon temperature

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Abstract
We study the steady state of the coupled-quasiparticle pair phonon system in a superconducting film in the présence of an optical irradiation for various strengths of the light. A numerical solution of the coupled equations is performed, the quasiparticle distribution being represented by a Fermi-Dirac distribution with an effective temperature T*. It is shown that the quantitative response of the superconducting film to the drive depends strongly on the imposed conditions : intensity of the drive, phonon escape time. The deviation from equilibrium of the phonon distribution cannot generally be ignored. A single phonon temperature can never be defined over the whole range of phonon frequencies. However, the temperature of phonons of energy larger than 2 Δ is well approximated by the quasiparticle effective temperature T* in many cases. The maximum deviation from equilibrium of the phonon spectrum may occur for ħω ≷2 Δ as well as for ħω = 2 Δ