Single particle polariton properties in doped quantum well microcavities: role of the Fermi edge singularity and Anderson orthogonality catastrophe

A theoretical investigation of the single particle polariton properties for a microcavity embedding a charged quantum well is presented. The electron gas optical susceptibility is calculated numerically using the method devised by Combescot and Nozi\`eres. The role of many-body effects, such as the Fermi edge singularity and Anderson orthogonality catastrophe, in the polariton formation is elucidated. By tuning the light-matter coupling the short time behaviour of the electron gas response function is probed and comparison with earlier results only using the long time response are made. Various single particle polariton properties such as the Rabi splitting, line shape, Hopfield coefficients and effective mass are discussed. These are experimentally accessible quantities and thus allow for a comparison with the presented theory.