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

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.033833· OSTI ID:21408513

Sindelka, Milan ^[1]

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1. Department of Physics and Minerva Center for Non-Linear Physics of Complex Systems, Technion - Israel Institute of Technology, Haifa IL-32000 (Israel)

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 Schroedinger 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.

• OSTI ID: 21408513
• Journal Information: Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.033833; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
EMISSION
EQUATIONS OF MOTION
HARMONIC GENERATION
INTERACTIONS
LASER RADIATION
LASERS
MATTER
PHOTONS
PULSES
QUANTUM ELECTRODYNAMICS
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SPECTRA
APPROXIMATIONS
BOSONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FREQUENCY MIXING
MASSLESS PARTICLES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
RADIATIONS
WAVE EQUATIONS