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Physical Review A

Spontaneous photon emission in isolated-core excited Rydberg systems and dynamics of electronic wave packets

O. Zobay, G. Alber

Published Dec 1, 1996• 8 citations
Publisher

Abstract

In isolated-core excited Rydberg systems the destruction of quantum coherence by spontaneous emission of photons is investigated. For this purpose a theoretical description is developed which is based on a decomposition of the atomic density operator into N-photon contributions. Using methods from multichannel quantum defect theory, the relevant atomic transition amplitudes are represented in the form of semiclassical path representations which are associated with repeated returns of the Rydberg electron to the ionic core. Apart from numerical advantages, this approach also yields a clear physical picture of the intricate interplay between the incoherent photon emission process, the coherent laser-modified electron correlation effects, and the semiclassical aspects of the dynamics of the Rydberg electron. Various examples of this interplay are analyzed within the framework of the developed theoretical tools. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.5361

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In isolated-core excited Rydberg systems the destruction of quantum coherence by spontaneous emission of photons is investigated. For this purpose a theoretical description is developed which is based on a decomposition of the atomic density operator into N-photon contributions. Using methods from multichannel quantum defect theory, the relevant atomic transition amplitudes are represented in the form of semiclassical path representations which are associated with repeated returns of the Rydberg electron to the ionic core. Apart from numerical advantages, this approach also yields a clear physical picture of the intricate interplay between the incoherent photon emission process, the coherent laser-modified electron correlation effects, and the semiclassical aspects of the dynamics of the Rydberg electron. Various examples of this interplay are analyzed within the framework of the developed theoretical tools. \textcopyright{} 1996 The American Physical Society.
Nondispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states, and show that the elastic incoherent component (occurring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single-photon emissions and the associated rates in the ``harmonic approximation,'' i.e., when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum-mechanical calculations, which validates the analytical approach.
It is shown that semiclassical path representations provide a well-suited framework for the description of the diffraction of Rydberg atoms by laser light. They allow one to relate the momentum exchange between the atomic center-of-mass motion and the laser field directly to elementary laser-assisted collisions between the excited Rydberg electron and the ionic core. Thus besides a convenient calculational tool they provide also direct physical insight into the underlying internal dynamics of the Rydberg atoms.
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.
We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.
The momentum exchange between a standing wave laser field and an atomic center-of-mass is dominated by the internal dynamics of an atomic electron in the exciting laser field. Rydberg atoms are one of the simplest physical systems where the dependence of this radiative force on the electronic dynamics can be investigated in detail. The characteristics of the momentum transfer between an atomic center-of-mass and a standing wave laser field strongly depend on whether the “particle” or the “wave” aspect of the electronic dynamics prevail. In this review recent theoretical advances in the description of the mechanical action of laser light on Rydberg atoms are discussed. These advances have become possible by the application of semiclassical path integral techniques with respect to the electronic dynamics which clearly exhibit the “particle” and “wave” aspects of this momentum transfer.
The formation of atom-optical gratings induced by multiphoton excitation of Rydberg states is discussed for fast atoms. With the help of semiclassical path-integral methods the correlation between the dynamics of a laser-excited Rydberg electron and the momentum transferred to the atomic center of mass in a spatially modulated laser field is exhibited quantitatively. These types of laser excitation processes might offer new perspectives for the realization of atomic multiple beam splitters and for atom-lithographic applications.