Canonical Transformation Approach to the Ultrafast Non-linear Optical Dynamics of Semiconductors

TL;DR

This paper introduces a canonical transformation method to analyze the ultrafast nonlinear optical response of semiconductors, accounting for many-particle Coulomb correlations and providing a clear physical interpretation.

Contribution

It develops a novel theoretical framework using Van Vleck canonical transformation to incorporate many-body Coulomb effects in ultrafast nonlinear optics of semiconductors.

Findings

Maps nonlinear response to linear response of a dressed system

Accounts for many-body Coulomb effects up to arbitrary order

Provides intuitive interpretation of nonlinear optical phenomena

Abstract

We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the ``bare'' system onto the linear response of a ``dressed'' system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.