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

Abstract

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 $\\phi$ 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 $2\\pi$ increment of $\\phi$, 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.