Dynamical Coulomb blockade of multiple Andreev reflections

We analyze the dynamical Coulomb blockade of multiple Andreev reflections (MAR) in a superconducting quantum point contact coupled to a macroscopic impedance. We find that at very low transmission the blockade scales as $n^2$ with $n = {Int}(2\Delta/eV)$, where $V$ is the bias voltage and $\Delta$ is the superconducting gap, as it would correspond to the occurrence of "shots" of charge $ne$. For higher transmission the blockade is reduced both due to Pauli principle and to elastic renormalization of the MAR probability, and for certain voltage regions it may even become an "antiblockade", i.e. the current is enhanced due to the coupling with the electromagnetic environment.