Beyond linear response theory for intensive light-matter interactions: Order formalism and ultrafast transient dynamics

Abstract

Recently constructed radiation sources deliver brilliant, ultrashort coherent radiation fields with which the material's response can be investigated on the femtosecond to attosecond time scale. Here, we develop a theoretical framework for the interaction of the material's electrons with such intensive, short radiation pulses. Our theory is based on the time evolution of the electron density matrix, as defined through the Liouville-von Neumann equation. The latter equation is solved here within the framework of the response theory, incorporating the perturbing field in higher orders. An analytical tool, called the order notation, is developed, which permits the explicit calculation of the arising $n$th-order operatorial convolutions. As examples of the formalism, explicit expressions for several optical phenomena are worked out. Through the developed theory presented here, two fundamental results are achieved: first, the perturbing field to higher than linear orders is included in an elegant and compact way, allowing to treat highly brilliant light, and, second, the complete transient time response on the subfemtosecond scale is analytically provided, thus dropping the adiabatic approximation commonly made in standard linear response theory.