A Coherent Two-Level System in a Superconducting Single-Electron Transistor Observed Through Photon-Assisted Cooper-Pair Tunneling

A coherent two-level system can be constructed in an ultrasmall Josephson-junction circuit, where two charge states are coupled by single Cooper-pair tunneling. To investigate coherence and decoherence in the two-level system, we have measured dc current through a voltage-biased superconducting single-electron transistor. Under microwave irradiation, a current due to photon-assisted Cooper-pair tunneling is induced, which serves as a useful experimental tool for spectroscopic study of the energy levels in the two-level system. We observed energy-level splitting, which is evidence of the coherent superposition of the two charge states.