Polariton formation in a microcavity with a doped quantum well: Roles 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 [J. Phys. (Paris) 32, 913 (1971)]. 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 behavior of the electron-gas response function is probed, and comparisons 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.