Time-dependent transport of electrons through a photon cavity

We use a non-Markovian master equation to describe the transport of Coulomb-interacting electrons through an electromagnetic cavity with one quantized photon mode. The central system is a finite-parabolic quantum wire that is coupled weakly to external parabolic quasi-one-dimensional leads at t=0. With a stepwise introduction of complexity to the description of the system and a corresponding stepwise truncation of the ensuing many-body spaces, we are able to describe the time-dependent transport of Coulomb-interacting electrons through a geometrically complex central system. We take the full electromagnetic interaction of electrons and cavity photons without resorting to the rotating-wave approximation or reduction of the electron states to two levels into account. We observe that the number of initial cavity photons and their polarizations can have important effects on the transport properties of the system. The quasiparticles formed in the central system have lifetimes limited by the coupling to the leads and radiation processes active on a much longer time scale.