  Experimental insight into the elementary processes underlying charge transfer
across interfaces has blossomed with the wide-spread availability of ultra-high
vacuum set-ups that allow the preparation and characterization of solid
surfaces with well-defined molecular adsorbates over a wide ranges of
temperatures. Thick layers of molecular adsorbates or heterostructures of 2D
materials generally preclude the use of electrons or atoms as probes in such
characterization. However with linear photon-in/photon-out techniques it is
often challenging to assign the observed optical response to a particular
portion of the interface. We and prior workers have demonstrated in work under
ambient conditions that by full characterization of the symmetry of the second
order nonlinear optical susceptibility, i.e. the $\chi^{(2)}$, in sum frequency
generation (SFG) spectroscopy, this problem can be overcome. Here we describe
an ultra-high vacuum system built to allow conventional UHV sample preparation
and characterization, femtosecond and polarization resolved SFG spectroscopy,
the azimuthal sample rotation necessary to fully describe $\chi^{(2)}$ symmetry
and with sufficient stability to allow scanning SFG microscopy. We demonstrate
these capabilities in proof-of-principle measurements on CO adsorbed on Pt(111)
and of the clean Ag(111) surface. Because this set-up allows both full
characterization of the nonlinear susceptibility and the temperature control
and sample preparation/characterization of conventional UHV set-ups we expect
it to be of great utility in investigation of both the basic physics and
applications of solid, 2D material heterostructures.
