Relaxation of coherent excited states of a superconductor to a superconducting reservoir

The effect of relaxation to a superconducting reservoir on coherent excited states of a superconductor that appear under irradiation by a microwave signal [A.V. Semenov et al., Phys. Rev. Lett. 117, 047002 (2016)] and can be destructed because of tunnel relaxation to a normal metal reservoir [A.V. Semenov et al., http://arxiv.org/abs/1801.03311] has been theoretically studied. A thin diffuse superconductor strip in tunnel contact with a diffuse superconducting reservoir is considered as a model. The strip is irradiated by a microwave signal with the frequency that is much higher than the normalized signal intensity but is much lower than the absolute value of its order parameter. The spectral functions of the superconducting strip and the distribution function of quasiparticles in it have been calculated. It has been demonstrated that the effect of relaxation on coherent excited states of the superconducting strip is significantly weakened when the absolute value of the order parameter of the superconducting reservoir tends to the absolute value of the order parameter of the superconducting strip.