Quantum fluctuations in an anharmonic superconducting circuit enable frequency conversion of individual incoming photons. This effect, linear in the photon beam intensity, leads to ramifications for the standard input-output circuit theory. We consider an extreme case of anharmonicity in which photons scatter off a small set of weak links within a Josephson junction array. We show that this quantum impurity displays Kondo physics and evaluate the elastic and inelastic photon scattering cross sections. These cross sections reveal many-body properties of the Kondo problem that are hard to access in its traditional fermionic version.
The Kondo effect refers to the screening of a spin-1/2 impurity by a cloud of conduction electrons, then forming a many-body Fermi liquid ground state. Theoretical calculations suggest that the Kondo resonance can interact with light and should give rise to a $\ensuremath{\pi}$-phase shift of the photon signal in the case where the ground state is a Fermi liquid. This $\ensuremath{\pi}$-phase shift of light is driven from the Korringa-Shiba relation of quantum impurity Fermi-liquid ground states. We report the first observation of such a $\ensuremath{\pi}$-phase shift in a graphene double quantum dot within a circuit quantum electrodynamics architecture where the microwave photons couple to the pseudospin or charge degrees of freedom. We study the evolution of the $\ensuremath{\pi}$-phase shift as a function of temperature and bias voltage. The observed Kondo temperature ${T}_{K}\ensuremath{\sim}550\phantom{\rule{0.16em}{0ex}}\text{mK}$ is in agreement with dc conductance measurements. All our results support the formation of a Kondo resonance located above the Fermi level of the electronic reservoirs with the occurrence of an
SU(4) Fermi-liquid ground state. We finally study how the Kondo-photon interaction can be tuned by inter-dot electron tunnel coupling strengths. Our findings may contribute to a better understanding of many-body physics in hybrid circuit systems, and open up applications in atomic thin materials from the light-matter interaction.