Electron tunneling through hybrid superconducting-normal quantum point contacts under microwave radiation

We present a theoretical analysis for photon-assisted electron tunneling through a hybrid superconducting-normal quantum point contact (QPC) consisting of a superconducting lead (S), a normal two-level quantum dot (N), and a normal lead (N). Using single particle non-equilibrium Green's function formalism, we incorporate Floquet basis in the Nambu space and solve the Green's function with finite matrix truncation to obtain the transport properties numerically. Based on the proposed method, we studied the effects of photon-induced single-level oscillations and quantum transition between two levels on the current-voltage (I-V) characteristics of a superconducting QPC. For the single level case, the main dc resonance in the I-V curve remains unchanged regardless of the frequency and amplitude of the radiation, and a series of secondary resonances due to multi-photon processes are present. When the transition between two levels ($\epsilon_{1}$, $\epsilon_{2}$) is taken into account and level oscillations are neglected, photons only have significant effects at Rabi resonance when $\hbar\omega=(\epsilon_{2}-\epsilon_{1})$. At Rabi resonance, the main dc resonance splits into two, and the separation between them is determined by the coupling strength of the two levels.