Phys. Rev. Lett. 111, 053601 (2013)
We investigate the effective interaction between two microwave fields, mediated by a transmon-type superconducting artificial atom which is strongly coupled to a coplanar transmission line. The interaction between the fields and atom produces an effective cross–Kerr coupling. We demonstrate average cross–Kerr phase shifts of up to 20 degrees per photon with both coherent microwave fields at the single-photon level. Our results provide an important step toward quantum applications with propagating microwave photons.