Approaching ideal rectification in superconducting diodes through multiple Andreev reflections

We analyze the rectification properties of voltage-biased Josephson junctions exhibiting the superconducting diode effect. Taking into account multiple Andreev reflection (MAR) processes in our scattering theory, we consider a short weak link of arbitrary transparency between two superconductors with finite Cooper pair momentum $2q$. In equilibrium, the diode efficiency is bounded from above in this model, with maximal efficiency ${\eta }_0\approx 0.4$. Out of equilibrium, we find a rich subharmonic structure in the current-voltage curve. For high transparency and low bias voltage $V$, the rectification efficiency $\eta (V)$ approaches the ideal value $\eta =1$ for $q\xi \to 1$ (with coherence length $\xi$).