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

Abstract

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