Coupling mechanism between microscopic two-level system and superconducting qubits

We propose a scheme to clarify the coupling nature between superconducting Josephson qubits and microscopic two-level systems. Although dominant interest in studying two-level systems was in phase qubits previously, we find that the sensitivity of the generally used spectral method in phase qubits is not sufficient to evaluate the exact form of the coupling. On the contrary, our numerical calculation shows that the coupling strength changes remarkably with the flux bias for a flux qubit, providing a useful tool to investigate the coupling mechanism between the two-level systems and qubits.