Plasmonics has attracted the interest of the scientific community mainly due to ability of metallic nanostructures to squeeze light to the nanosale far beyond the diffraction limit of classical optics. The main principle of the nanofocusing property of metallic nanoparticles consists in the conversion of electromagnetic waves into collective excitations of electrons, so-called plasmons, which can be understood as special optical nanocavities which can mediate extraordinarily strong interaction of light with e.g. molecules. The theoretical description of the optical properties of such extremely small plasmonic cavities often surpasses the limits of classical physics and requires a quantum mechanical treatment. To that end our group participates in the development of the many-body description of plasmonic excitations as a condensed matter excitation within the framework of Time-Dependent Density Functional Theory (TDDFT). In close collaboration with the group of Andrei Borissov in Orsay (Paris), we address effects such as quantum tunneling of electrons in nano-sized gaps, effects of non-local screening, coupling of plasmons to the electron-hole continuum or atomistic effects driving the localization of light down to the atomic scale. Due to the computational complexity of quantum mechanical methods it is impossible to treat large systems containing millions of free electrons. One of the efforts of our group therefore consists in developing effective semiclassical models that can bridge the gap between the full quantum and purely classical descriptions of the electromagnetic response.
Furthermore, the interaction of plasmons with molecular excitations might also require a treatment that properly quantize the electromagnetic field associated with the plasmons, in order to properly address the coherences and the quantum dynamics of the system. The field-quantization of a plasmonic cavity can be based on quantum electrodynamics (QED). QED is a suitable platform to deal with the quantum statistics of the plasmonic and molecular excitations and effectively treats the interaction with a reservoir. All these aspects are necessary for a correct description of e.g. quantum fluctuations, decay processes, or collective light emission from molecules. In our group we thus apply general methods of QED to describe the coupling of plasmons with molecules in (sub)nanometric cavities, addressing phenomena such as the fluctuation-driven spontaneous emission of molecules or surface-enhanced Raman scattering, to reveal novel non-classical processes and phenomena.