  Superconductivity is commonly described as a macroscopic quantum phenomenon.
However, it arises from microscopic mechanisms occurring at the nanometer scale
as illustrated, for example, by the non-trivial pairing in unconventional
superconductors. More recently, also local interactions with superconductors in
the context of Majorana fermions became of interest. A very direct way to study
the atomic scale properties of superconductors is given by the combination of
the Josephson effect with scanning tunneling microscopy (STM), also referred to
as JSTM. Here, the critical Josephson current serves as a direct local probe of
the superconducting ground state and may reveal valuable information that is
often inaccessible when studying quasi-particle excitation spectra. We show
that we can extract local values of the critical Josephson current from JSTM
measurements in the dynamical Coulomb blockade regime. Furthermore, we
experimentally determine the regime of sequential Cooper pair tunneling, which
is in accordance to theoretical predictions. Our study presents new insights on
the tunneling mechanisms in Josephson junctions and lays the basis for the
implementation of JSTM as a versatile probe for superconductivity.
