Cavity-assisted mesoscopic transport of fermions: Coherent and dissipative dynamics

We study the interplay between charge transport and light-matter interactions in a confined geometry by considering an open, mesoscopic chain of two-orbital systems resonantly coupled to a single bosonic mode close to its vacuum state. We introduce and benchmark different methods based on self-consistent solutions of nonequilibrium Green's functions and numerical simulations of the quantum master equation, and derive both analytical and numerical results. It is shown that in the dissipative regime where the cavity photon decay rate is the largest parameter, the light-matter coupling is responsible for a steady-state current enhancement scaling with the cooperativity parameter. We further identify different regimes of interest depending on the ratio between the cavity decay rate and the electronic bandwidth. Considering the situation where the lower band has a vanishing bandwidth, we show that for a high-finesse cavity, the properties of the resonant Bloch state in the upper band are transferred to the lower one, giving rise to a delocalized state along the chain. Conversely, in the dissipative regime with low-cavity quality factors, we find that the current enhancement is due to a collective decay of populations from the upper to the lower band.