  We use an on-chip superconducting resonator as a sensitive meter to probe the
properties of graphene double quantum dots at microwave frequencies.
Specifically, we investigate the charge dephasing rates in a circuit quantum
electrodynamics architecture. The dephasing rates strongly depend on the number
of charges in the dots, and the variation has a period of four charges, over an
extended range of charge numbers. Although the exact mechanism of this fourfold
periodicity in dephasing rates is an open problem, our observations hint at the
fourfold degeneracy expected in graphene from its spin and valley degrees of
freedom.
