  With recent experiments investigating the optical properties of progressively
smaller plasmonic particles, quantum effects become increasingly more relevant,
requiring a microscopic description. Using the density matrix formalism we
analyze the photo-excited few-electron dynamics of a small nanosphere.
Following the standard derivation of the bulk plasmon we particularly aim on
elucidating the role of the Coulomb interaction. Calculating the dielectric
susceptibility spectrum in the linear optical response we find discrete
resonances resulting from a collective response mediated by the Coulomb
interaction between the electrons. In the nonlinear regime, the occupations of
the system exhibit oscillations between the interacting eigenstates. Our
approach provides an ideal platform to study and explain nonlinear and quantum
plasmonics, revealing that the photo-excited dynamics of plasmonic nano spheres
has similarities with and combines characteristics of both, the well-known
two-level Rabi dynamics, and the collective many-electron behavior typical of
plasmons.
