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

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