Voltage staircase in a current-biased quantum-dot Josephson junction

We calculate the current-voltage ($I\ensuremath{-}V$) characteristic of a Josephson junction containing resonant level in weakly coupled regime (resonance width small compared to superconducting gap). The phase $\ensuremath{\phi}$ across becomes time dependent response DC current bias. Rabi oscillations Andreev levels produce staircase $I\ensuremath{-}V$ characteristic. number voltage steps counts per $2\ensuremath{\pi}$ increment $\ensuremath{\phi}$, providing way probe coherence qubit absence any external AC driving. phenomenology is same as Majorana-induced Shapiro topological junctions Choi et al. [Phys. Rev. B 102, 140501(R) (2020)]---but now for nontopological qubit.