  Second-order nonlinear optical processes do not manifest in the bulk of
centrosymmetric materials, but may occur in the angstroms-thick layer at
surfaces. At such length-scales, quantum mechanical effects come into play
which could be crucial for an accurate description of plasmonic systems. In
this article, we develop a theoretical model based on the quantum hydrodynamic
description to study free-electron nonlinear dynamics in plasmonic systems. Our
model predicts strong resonances induced by the spill-out of electron density
at the metal surface. We show that these resonances can boost second-harmonic
generation efficiency up to four orders of magnitude and can be arbitrarily
tuned by controlling the electron spill-out at the metal surface with the aid
of thin dielectric layers. These results offer a possibility to artificially
increase nonlinear susceptibilities by engineering optical properties at the
quantum level.
