Third order response to a multifrequency photon field in semiconductors

This paper contains a detailed calculation of the photoinduced current density at third order in the coupling between a semiconductor and a multifrequency photon field, starting from its standard textbook expression which reads in terms of a triple commutator. Due to a major intrinsic problem linked to this triple commutator, such a derivation has been made possible quite recently only, thanks to the tools developed in the composite-boson many-body theory we have recently constructed. The photoinduced current density is shown to ultimately read in a compact form, in terms of the “Pauli scatterings” and “Coulomb scatterings” for exciton-exciton interactions introduced in this theory. Representation of this third order response in Shiva diagrams, which visualize interactions between excitons, is also given to better grasp the physics of the various contributions.