  Mesoscopic systems constitute appealing platforms to study many-body physics
with light and matter degrees of freedom. 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. The Kondo resonance produces a
phase shift in the transmitted electronic wave packet which depends on the
symmetry and nature of the many-body ground state. Theoretical calculations
suggest that the Kondo resonance can interact with the irradiation photon field
and should give rise to a {\pi}-phase shift of the photon signal in the case
where the ground state is a Fermi liquid. This {\pi}-phase shift of microwave
photon is driven from the Korringa-Shiba relation of quantum impurity
Fermi-liquid ground states. We report the first observation of such a
{\pi}-phase shift in a graphene double quantum dot within a circuit quantum
electrodynamics architecture where the microwave photons couple to the
pseudo-spin or charge degrees of freedom. The observed Kondo temperature TK ~
550 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 and the occurrence of an SU(4) Fermi-liquid ground state.
We finally study how the Kondo-photon interactions can be tuned by inter-dot
electron tunnel coupling strengths. Our experimental achievements may
contribute to a better understanding of many-body physics in hybrid circuit
systems, and open up new applications in atomic thin materials from the
light-matter interaction.
