Derivation of coupled Maxwell-Schrodinger equations describing matter-laser interactionfrom first principles of quantum electrodynamics

摘要

We study the general problem of matter-laser interaction within the framework of nonrelativistic quantumelectrodynamics, with particular emphasis on strong laser field effects. Consequently, we formulate a well-definedapproximation leading in a straightforward manner toward the conventional semiclassical mode of description.Namely, we arrive naturally to two coupled equations of motion: (i) the Schrodinger equation which governs thequantum dynamics of an atomic system driven by classically described radiation field (composed of an incominglaser pulse plus radiation emitted from the atom), and (ii) the classical Maxwell wave equation which describes theemission of radiation from the mentioned atomic source. Employing the formalism of adiabatic Floquet theory,we derive a simple criterion of validity of the just described semiclassical approach. It shows that the semiclassicaltreatment is justified in most situations. On the other hand, it turns out that the semiclassical approximation breaksdown completely in certain special but realistic cases, regardless of the fact that the incoming laser pulse contains ahuge number of photons. Under such special circumstances, we anticipate new effects arising due to the quantizednature of the radiation field, to be observable, for example, in harmonic generation spectra. Our considerationsare illustrated more explicitly using a simple model of a two-level atom strongly driven by a laser. The quantumdynamics of this model problem is resolved within the framework of quantum electrodynamics while adoptingwell-defined and physically justifiable approximations. As an outcome, analytic formulas are found serving asa quantitative criterion of (non)applicability of the semiclassical approach and demonstrating the breakdown ofsemiclassical theory under well-defined conditions. An illustrative numerical calculation is provided.