Inducing and detecting geometric phases with superconducting quantum circuits

We propose a theoretically feasible scheme for controllably inducing and effectively detecting geometric phases by a superconducting circuit device. Only by adjusting the microwave pulses applied to the considered circuit, the non-Abelian and Abelian geometric phases can be induced controllably. Through considering the population difference after two composite evolutions, the noncommutative or commutative features of geometric phases can be explicitly shown. We address the scenarios of physical implementations with the available technology. Thus the scheme may offer a potential approach for synthetically investigating geometric phases with Josephson circuits.