Equation-of-motion technique for finite-size quantum-dot systems: Cluster expansion method

Abstract

An equation-of-motion based theory for the description of light emission from multilevel semiconductor quantum dots (QDs) is presented. It accounts for electronic excitations in the presence of Coulomb interaction, leading to multiexciton states, and their coupling to the quantized electromagnetic field. The two key aspects of this work concern (i) the combination of an exact treatment of the electronic degrees of freedom with an approximate approach for the photonic degrees of freedom that is based on the cluster expansion technique and (ii) the consistent incorporation of scattering and dephasing due to the coupling to delocalized electronic states and phonons into the equations of motion via Lindblad terms. Differences to previously used theories are discussed and results of the theory are shown for free-space emission, where multiexciton spectra are shown, and for emission into a single high-$Q$ cavity mode. In the latter case, a full solution of the von-Neumann equation is used to benchmark the proposed theory, which we term ``finite-size hierarchy'' (FSH) method.