  We study plasmonic excitations in the limit of few electrons, in one-atom
thick sodium chains, and characterize them based on collectivity. We also
compare the excitations to classical localised plasmon modes and find for the
longitudinal mode a quantum-classical transition around 10 atoms. The
transverse mode appears at much higher energies than predicted classically for
all chain lengths. The electric field enhancement is also considered which is
made possible by considering the effects of electron-phonon coupling on the
broadening of the electronic spectra. Large field enhancements are possible on
the molecular level allowing us to consider the validity of using molecules as
the ultimate small size limit of plasmonic antennas. Additionally, we consider
the case of a dimer system of two sodium chains, where the gap can be
considered as a picocavity, and we analyse the charge-transfer states and their
dependence on the gap size as well as chain size. Our results and methods are
useful for understanding and developing ultra-small, tunable and novel
plasmonic devices that utilise quantum effects that could have applications in
quantum optics, quantum metamaterials, cavity-quantum electrodynamics and
controlling chemical reactions, as well as deepening our understanding of
localised plasmons in low dimensional molecular systems.
