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Journal of Physics B Atomic Molecular and Optical Physics

Polarization properties of multiphoton processes in quantum systems with large angular momentum

A. A. Apolonsky, K. A. Nasyrov, Anatolii M. Shalagin

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/13/304

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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.
We develop a theory that describes the interaction of radiation and multilevel particles on the basis of the classical description of the orientation of angular momentum. For examples of application of this theory we take the problems of stimulated Raman scattering and of parametric generation of light in four-wave mixing. We find that the efficiency of the radiation processes largely depends on the polarization of the pump waves and on the types of optical transitions (Δ J ) and to a much lesser extent on the value of the angular momentum J . We also explain some polarization phenomena observed in experiments on four-wave mixing.
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The Wigner representation of angular-momentum orientation in the classical limit on $J\ensuremath{\gg}1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\stackrel{\ensuremath{\rightarrow}}{J}J$ or $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, 1/J,1/\sqrt{J},1/J​, of the angular-momentum orientation. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ or $\stackrel{\ensuremath{\rightarrow}}{J}J,$ transition particles come into ``dark'' states while for the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition they occupy the ``brightest'' state. In the presence of a nonzero magnetic field, particles with $\stackrel{\ensuremath{\rightarrow}}{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition the directions of the angular momentum form a cone around the magnetic field.
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.
A theory of resonantly enhanced degenerate four-wave mixing in two-level systems including the effects of atomic and photon angular momentum is presented in the absence of pump-induced saturation of the transition. It is shown that there exist three distinct quantum-mechanical amplitudes leading to the third-order polarization density. These quantum-mechanical amplitudes are shown to be sensitive to the states of polarization of the incident fields. The quantum-mechanical transport equation in the mmm representation is used to calculate the output signal in the various regimes of laser detuning, atomic linewidth, and polarization states of the radiation field for collinear interaction.
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.