  Josephson junctions operated in the dynamical Coulomb blockade regime
recently gained an significant amount of attention as central building block in
concepts to demonstrate the non-Abelian character of Majorana fermions. Its
physical properties are strongly affected by the intimate interplay of
intrinsic quantum fluctuations and environmentally-induced quantum fluctuations
each of which promoting different Cooper pair transport mechanisms at small
voltages around zero. To shed light on the detailed transport mechanisms
occurring in this type of junction, we performed voltage-biased measurements on
the small-capacitance Josephson junction of a scanning tunneling microscope at
milli-Kelvin temperatures. The low voltage-regime of experimental
current-voltage characteristics can be modeled by the two complementary
descriptions of phase coherent and incoherent Cooper pair transport, signaling
the occurrence of qualitatively different transport mechanisms. This
observation receives further support from analyzing the calculated Fano factor
of the current noise as a probe for correlations in Cooper pair transport,
following a theoretical proposal. Together our experimental observations and
related data analysis provide a clear signature of coherent Cooper pair
transport along with the absence of perfect charge quantized transport around
zero voltage, as well as of incoherent Cooper pair transport towards higher
voltages.
