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Laser Physics Letters

Limitations of the semiclassical approach for the problem of two-level atomic ensemble emission in a resonant laser field

Anna V. Bogatskaya, A. M. Popov

Published Aug 6, 2020• 2 citations
Publisher

Abstract

Abstract Both quantum-electrodynamical (QED) and semiclassical approaches are applied to study the spontaneous emission of an atom or atomic ensemble driven by the strong external laser field. It is demonstrated that the semiclassical approach typically used for analyzing the emission of dressed atomic systems is inconsistent with the QED approach and does not provide a proper description of the emission of two-level atoms in a strong external laser field. That is, aside from a situation where the external radiation is nonresonant, weak enough and does not cause the essential population of the excited atomic level.

DOI
10.1088/1612-202x/aba198

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Abstract Both quantum-electrodynamical (QED) and semiclassical approaches are applied to study the spontaneous emission of an atom or atomic ensemble driven by the strong external laser field. It is demonstrated that the semiclassical approach typically used for analyzing the emission of dressed atomic systems is inconsistent with the QED approach and does not provide a proper description of the emission of two-level atoms in a strong external laser field. That is, aside from a situation where the external radiation is nonresonant, weak enough and does not cause the essential population of the excited atomic level.
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 Schr\"odinger 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.
Analytical expressions for the quasienergies and corresponding semiclassical dressed states are obtained for a two-level quantum system driven by a nonresonant and/or strong laser field in a coherent state. These expressions are of first order in a proper perturbative expansion, and already contain all the relevant physical information on the dynamical and spectroscopic properties displayed by these systems under such particular conditions. The influence of the laser field parameters on transition frequencies, selection rules, and line intensities is easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.
Spontaneous emission of the quantum system driven by a high intensity classical laser field is analyzed. The study is based on the accurate consideration of quantum system interaction with vacuum quantized field modes in the first order of perturbation theory, while the intense laser field is considered classically beyond the perturbation theory. It is demonstrated that the spectrum of the spontaneous emission can be used for analyzing of the strong-field dynamics and structure of the energy spectrum of the atomic system. The obtained data are compared with that obtained in the frames of semiclassical approximation typically used for analyzing of the strong-field dynamics. It is found that the applicability of the semiclassical approach is strictly limited.
A new approach to the study of the spontaneous emission of the quantum system driven by a high-intensity laser field is developed. This approach is based on the accurate consideration of quantum system interaction with vacuum quantized field modes in the first order of perturbation theory, while the intense laser field is considered classically beyond the perturbation theory which allows to observe any-order stimulated processes governed by classical field. The proposed approach is applied to the study of a number of quantum systems in intense laser field. The obtained data are compared with those obtained in the frames of semiclassical approximation typically used for analyzing of the strong-field dynamic. It is found that the applicability of the semiclassical approach is strictly limited. It is valid for calculation of transitions to the initially populated state only if the population of this state is close to unity during the pulse and in the after-pulse regime. If its population is depleted, the semiclassical approach fails.
A semiclassical radiation theory is developed in which the spontaneous emission field of a two-level atom is a quantum entity represented by atomic operators acting in the Hilbert space of the atomic states. The theory is applied to an investigation of the coherence properties of spontaneous emission. It is found that incoherent and coherent components can be identified in the emission field, the former dominating in the early stages of the decay from the excited state and the latter dominating in the later stages or in the emission from a weakly excited atom. The single-atom coherence properties are shown to lead to well-known superradiance phenomena in the spontaneous emission from an assembly of similar atoms. The paper does not use the theory of quantum electrodynamics; it builds on knowledge at the undergraduate level of classical radiation theory and the quantum mechanics of atoms.
Analytical expressions for the semiclassical dressed states and corresponding quasienergies are obtained for a two-level quantum system driven by a non-resonant and/or strong laser field in a coherent state. These expressions are of first order in a proper perturbative expansion, and already contain all the relevant physical information on the dynamical and spectroscopic properties displayed by these systems under such particular conditions. The influence of the laser field parameters on transition frequencies, selection rules and line intensities can be easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.