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Quantum fluctuations in an anharmonic superconducting circuit enablefrequency conversion of individual incoming photons. This effect, linear in thephoton beam intensity, leads to ramifications for the standard input-outputcircuit theory. We consider an extreme case of anharmonicity in which photonsscatter off a small set of weak links within a Josephson junction array. Weshow that this quantum impurity displays Kondo physics and evaluate the elasticand inelastic photon scattering cross sections. These cross sections revealmany-body properties of the Kondo problem that are hard to access in itstraditional fermionic version.

Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array