Effective dephasing theory of the optical Anderson transition as probed by four-wave-mixing spectroscopy

Abstract

A novel theory of quantum mechanical transport in disordered systems is developed. The theory is based on the effective dephasing approximation (EDA), in which the ensemble averaged Liouville space propagator is mapped into the propagator of an ordered lattice with an effective frequency-dependent dephasing rate. This generalized dephasing rate is determined self-consistently. This approach is applicable to strongly disordered systems and yields results that interpolate between the limits of coherent and incoherent excitation transport and that predict the optical analog of a metal–insulator phase transition (Anderson localization). Our results agree with the predictions of the scaling theory of the Anderson transition. We apply the EDA to the calculation of the transient grating signal from a crystal with an inhomogeneously broadened absorption spectrum (static, site energy disorder). The transient grating experiment is shown to be a sensitive probe of the optical Anderson transition.