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

TYPETheor./Math. Physics Seminar
Speaker:Dr. Milan Sindelk
Location:Lewiner Seminar Room (412)
Abstract:We study the general problem of matter-laser interaction within the framework of
nonrelativistic quantum electrodynamics, with particular emphasis on strong
laser field effects. Consequently, we formulate a well-defined approximation
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 the quantum dynamics of an atomic
system driven by classically described radiation field (composed of an incoming
laser pulse plus radiation emitted from the atom), and (ii) the classical
Maxwell wave equation which describes the emission 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 semiclassical treatment is justified in most
situations. On the other hand, it turns out that the semiclassical
approximation breaks down completely in certain special but realistic cases,
regardless of the fact that the incoming laser pulse contains a huge number of
photons. Under such special circumstances, we anticipate new effects arising
due to the quantized nature of the radiation field, to be observable, for
example, in harmonic generation spectra. Our considerations are illustrated
more explicitly using a simple model of a two-level atom strongly driven by a
laser. The quantum dynamics of this model problem is resolved within the
framework of quantum electrodynamics while adopting well-defined and physically
justifiable approximations. As an outcome, analytic formulas are found serving
as a quantitative criterion of (non) applicability of the semiclassical
approach and demonstrating the breakdown of semiclassical theory under
well-defined conditions. An illustrative numerical calculation is provided.