Optical Manifestations of the Electron-Electron Interaction

In this thesis, two optical manifestations of the electron-electron interaction are studied: the Fermi -edge singularity in doped quantum wells and quantum wires, and second-harmonic generation in mixed-valent compounds. First, we construct a theory of the Fermi-edge singularity that can systematically account for the finite mass of a hole created in the valence subband of a quantum well or quantum wire. The dynamical response for finite hole mass depends crucially on the dimensionality of the Fermi sea. Whereas in three dimensions the infrared divergence is suppressed, in two dimensions a one-over-square-root singularity survives, while in one dimension the spectrum is even more singular with recoil than without recoil. This explains the large optical singularities observed in quantum wires. Correlations change the prefactor, but not the exponent of the threshold behaviour in two and in three dimensions, while in one dimension, they affect neither the prefactor nor the exponent. Second, we apply our theory to the Frohlich polaron, a manifestation of the electron-phonon rather than the electron-electron interaction. The new method of calculating the Green's function removes unphysical features of the conventional cumulant expansion that had remained unnoticed in the literature up to now. Third, in an effort to investigate the impact of coherence on optical properties, we calculate the linear and nonlinear optical characteristics of mixed-valent compounds. Second -harmonic generation can only occur for solutions of the theoretical Falicov-Kimball model that have a built-in coherence between the itinerant d-electrons and localized f-holes. By contrast, second-harmonic generation cannot occur for solutions with f-site occupation as a good quantum number. The interaction between optically created quasiparticles leads to a threshold singularity in the absorption spectrum, and greatly enhances the second-harmonic conversion efficiency at half the gap frequency. As an experimental test of coherence we propose the measurement of the second-harmonic susceptibility of SmB_6..