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Lithuanian Journal of Physics

Photoexcitation of polarized atoms by polarized radiation

Alicija Kupliauskienė

Published Jan 1, 2004• 9 citations
Publisher

Abstract

An expression for the probability of the excitation of polarized atoms by polarized radiation is obtained by using the graphical technique of angular momentum. In the case of pure states, the applied method is an alternative to that of density matrix formalism. The obtained expression enables one to describe the polarization state of an excited atom and can be used to derive formulas for the special cases under specific experimental conditions as well as for the photoexcitation as the first step process. The application of obtained expressions for the description of multistep processes is discussed. The photoexcitation of unpolarized atoms by polarized radiation and polarized atoms by unpolarized radiation is considered as the examples of practical application of the obtained general expression.

DOI
10.3952/lithjphys.44102

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An expression for the probability of the excitation of polarized atoms by polarized radiation is obtained by using the graphical technique of angular momentum. In the case of pure states, the applied method is an alternative to that of density matrix formalism. The obtained expression enables one to describe the polarization state of an excited atom and can be used to derive formulas for the special cases under specific experimental conditions as well as for the photoexcitation as the first step process. The application of obtained expressions for the description of multistep processes is discussed. The photoexcitation of unpolarized atoms by polarized radiation and polarized atoms by unpolarized radiation is considered as the examples of practical application of the obtained general expression.
A method alternative to the density matrix formalism is applied to derive a general expression for the radiative decay probability following the photoionization of polarized atoms in two-step approximation. The graphical technique of the angular momentum theory is used for the integration over angular and spin variables. The general expression joining both steps of photoionization and fluorescence contains the possibility to investigate the polarization of all particles in the initial and final states and the angular distributions as well as angular correlations of photoelectrons and radiation. A simple way to get the expressions for special cases of the angular distribution and polarization of fluorescence radiation in the photoionization of randomly orientated and polarized atoms is given as an example of the practical application of the general formula.
We generalize an approach (previously proposed by two of the authors) to describe quantum systems with large angular momentum exposed to a radiation field. The approach exploits a transformation from the quantum-mechanical description to the classical one with respect to angular momentum orientation. The transformation is carried out through a density matrix representation similar to the well known Wigner representation for the translational degrees of freedom. The generalization opens up the possibility of describing the interaction of polychromatic radiation (i.e. a set of monochromatic components) with a quantum system when the spectral components of the radiation are resonant to different transitions of the system. It follows naturally from the obtained equations that if the solution of the problem within the framework of the model of nondegenerate states is known, then its generalization for the case of state degeneracy and accounting for polarization of interacting fields is given by the simplest operation. As an example, the proposed method is applied to stimulated Raman scattering and four-wave mixing. We pay special attention to those polarization features which, on the one hand, are interesting to experimentalists and, on the other hand, have not yet been given an adequate explanation in the literature.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
General expressions are derived and investigated for the degree of polarization of electrons as a result of resonant two-photon ionization of unpolarized atoms having the S state as the ground state. The exciting and ionizing electromagnetic fields have arbitrary degrees of polarization and directions of propagation. It is shown that in cases where the matrix elements of P → S transitions from the resonant state to the continuum predominante over the matrix elements of P → D transitions, completely polarized photoelectrons may be obtained. These cases are found for sodium and potassium atoms.
We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta Jg{J}_{g}Jg​ and Je{J}_{e}Je​ of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broadband radiation is given. We indicate various applications of these results.
In recent years interest has significantly quickened in investigation of nonlinear optical and spectroscopic phenomena in such unique objects as Rydberg atoms (the atoms in the energy states near the ionization limit) and van der Waals complexes (dimers). These objects are characterized, in particular, by that their energy states are strongly degenerate due to a large value of angular (rotational) momentum. Here, the problem arises of adequate theoretical description of experimental results, especially when polarization peculiarities of nonlinear radiation processes are considered. The problem is caused by the existence of a huge number of quantum magnetic sublevels of energy states, which are, in the general case, coherently coupled to each other and take part in the radiation processes. Figure 1 gives a vivid presentation of the problem arising even in such a seemingly simple case when one need describe the radiation transitions caused by a strong monochromatic field between two energy levels with large values of the angular momentum J. If the field polarization is arbitrary, the whole set of the magnetic sublevels turn out to be coupled by radiative transitions. Formally, the problem becomes essentially multilevel. In this case not only the hope fades of solving it analytically using the traditional quantum-mechanical approach, but the problems of numerical solution grow abruptly with increasing quantum number J as well. On the other hand, as is often the case, every cloud has a silver lining. With large J we approach the situation when the rotational motion of particles can be described classically. It turns out that the transition from the quantum description of orientation states of the angular momentum to the classical one simplifies the problem radically: it reduces to the problem of radiation processes in the simplest model of nondegenerate states. In this case the rotational motion manifests itself in a dependence of the density matrix elements on orientation angles of the angular momentum as on a parameter.