Effective gauge potentials induced by superconducting quantum circuits

We theoretically propose a scheme to induce non-Abelian and Abelian gauge potentials by the same superconducting circuit device. The level spacings of Cooper-pair box can be designed to resonantly match or largely detune from the mode frequencies of the one-dimensional transmission line resonators. We show the appearances of the effective gauge potentials via field quadrature operators. This scheme could help investigating the fundamental characteristics of the gauge theories with Josephson circuits.