Spectroscopy of Energy-Level Splitting between Two Macroscopic Quantum States of Charge Coherently Superposed by Josephson Coupling

We study Cooper-pair tunneling in a voltage-biased superconducting single-electron transistor under microwave irradiation. By tracing the peak positions of a photon-assisted Josephson-quasiparticle current as a function of the microwave frequency, we observe an energy-dispersion curve in the quasicharge space. This shows that energy-level splitting occurs between two macroscopic quantum states of charge coherently superposed by Josephson coupling.