Origin of Subharmonic Gap Structure of DC Current-Biased Josephson Junctions

The current-voltage characteristics of Josephson junctions exhibit a subharmonic gap structure (SGS), denoting jumps at specific voltages. While the prevalent multiple Andreev reflection theory matches the experimentally observed SGS, it is limited to a DC \emph{voltage} bias. For a DC \emph{current} bias, existing theories are restricted to low-transparency junctions and fail to capture the full SGS. We introduce a microscopic Floquet approach applicable for arbitrary transparencies, and recover the correct SGS for a DC \emph{current} bias. We provide a comprehensive understanding of SGS for a DC \emph{current} bias, which entails two-quasiparticle tunneling processes absent in existing theories, via two complementary perspectives: in the frequency domain, as generalised Andreev reflections absorbing multiple energies, and in the time domain, as the interference of non-equilibrium current pulses.