  We present a combined experimental and theoretical study of the proximity
effect in an atomic-scale controlled junction between two different
superconductors. Elaborated on a Si(111) surface, the junction comprises a Pb
nanocrystal with an energy gap of 1.2 meV, connected to a crystalline atomic
monolayer of lead with a gap of 0.23 meV. Using in situ scanning tunneling
spectroscopy we probe the local density of states of this hybrid system both in
space and in energy, at temperatures below and above the critical temperature
of the superconducting monolayer. Direct and inverse proximity effects are
revealed with high resolution. Our observations are precisely explained with
the help of a self-consistent solution of the Usadel equations. In particular,
our results demonstrate that in the vicinity of the Pb islands, the Pb
monolayer locally develops a finite proximity-induced superconducting order
parameter, well above its own bulk critical temperature. This leads to a giant
proximity effect where the superconducting correlations penetrate inside the
monolayer a distance much larger than in a non-superconducting metal.
