Characterization and control of matter by optical means is at the forefront of research both due to fundamental insights and technological promise. Theoretical modeling of periodically driven systems is a prerequisite to understanding and engineering nanoscale quantum devices for quantum technologies. Here, we develop a theory for transport and optical response of molecular junctions, open nonequilibrium quantum systems, under external periodic driving. Periodic driving is described using the Floquet theory combined with nonequilibrium Green's function description of the system. Light-matter interaction is modeled by employing the self-consistent Born approximation. A generic three-level model is utilized to illustrate the effect of the driving on optical and transport properties of junctions.

We introduce the notion, and develop the theory of local-noise spectroscopy (LNS) - a tool to study the properties of systems far from equilibrium by means of flux density correlations. As a test bed, we apply it to biased molecular junctions. This tool naturally extends those based on local fluxes, while providing complementary information on the system. As examples of the rich phenomenology that one can study with this approach, we show that LNS can be used to yield information on microscopic properties of bias-induced light emission in junctions, provide local resolution of intra-system interactions, and employed as a nano-thermometry tool. Although LNS may, at the moment, be difficult to realize experimentally, it can nonetheless be used as a powerful theoretical tool to infer a wide range of physical properties on a variety of systems of present interest.

We present a pedagogical review of the current density simulation in molecular junction models indicating its advantages and deficiencies in analysis of local junction transport characteristics. In particular, we argue that current density is a universal tool which provides more information than traditionally simulated bond currents, especially when discussing inelastic processes. However, current density simulations are sensitive to the choice of basis and electronic structure method. We note that while discussing the local current conservation in junctions, one has to account for the source term caused by the open character of the system and intra-molecular interactions. Our considerations are illustrated with numerical simulations of a benzenedithiol molecular junction.