Coherent excited states in superconductors due to a microwave field

We describe theoretically the depairing effect of a microwave field on diffusive s-wave superconductors. The ground state of the superconductor is altered qualitatively in analogy to the depairing due to a dc current. In contrast to dc-depairing the density of states acquires, for microwaves with frequency $\omega_0$, steps at multiples of the photon energy $\Delta\pm n\hbar\omega_0$ and shows an exponential-like tail in the subgap regime. We show that this ac-depairing explains the measured frequency shift of a superconducting resonator with microwave power at low temperatures.