Optical Properties of Few and Many Fröhlich Polarons from 3D to 0D

In this chapter I treat basic concepts and recent developments in the field of optical properties of few and many Fröhlich polarons in systems of different dimensions and dimensionality. The key subjects are: comparison of the optical conductivity spectra for a Fröhlich polaron calculated within the all-coupling path-integral based theory with the results obtained using the numerical Diagrammatic Quantum Monte Carlo method and recently developed analytical approximations. The polaron excited state spectrum and the mechanism of the optical absorption by Fröhlich polarons are analysed in the light of early theoretical models (from 1964 on) and of recent results. Further subjects are the scaling relations for Fröhlich polarons in different dimensions; the all-coupling path-integral based theory of the magneto-optical absorption of polarons; Fröhlich bipolarons and their stability; the many-body problem (including the electron-electron interaction and Fermi statistics) in the few- and many-polaron theory; the theory of the optical absorption spectra of many-polaron systems; the ground-state properties and the optical response of interacting polarons in quantum dots; non-adiabaticity of polaronic excitons in semiconductor quantum dots. Numerous examples are shown of comparison between Fröhlich polaron theory and experiments in high-T _c materials, manganites, silver halides, semiconductors and semiconductor nanostructures, including GaAs/AlGaAs quantum wells, various quantum dots etc. Brief sections are devoted to the electronic polaron, to small polarons and to recent extensions of Landau‘s concept, including ripplopolarons.