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Journal of Experimental and Theoretical Physics Letters

Polarization effects in recoil-induced resonances

L. V. Il’ichev

Published Oct 1, 2007• 5 citations
Publisher

Abstract

A model of the formation of recoil-induced resonances accompanying the interaction of an ensemble of slow atoms with a pair of plane light waves with different polarizations is constructed in the framework of the semiclassical approach to the description of the angular momentum of atoms. The approach used reduces the problem to the description of the resonances in the effective model of atoms with nondegenerate levels. The resonance amplitudes exhibit a strong dependence on the type of model used (with or without the inclusion of the degeneration of levels) and on the polarization of light waves. At the same time, the shape of the resonances that is normalized to unit amplitude from which the velocity distribution of atoms can be reconstructed is much less sensitive to the model type.

DOI
10.1134/s0021364007150040

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A model of the formation of recoil-induced resonances accompanying the interaction of an ensemble of slow atoms with a pair of plane light waves with different polarizations is constructed in the framework of the semiclassical approach to the description of the angular momentum of atoms. The approach used reduces the problem to the description of the resonances in the effective model of atoms with nondegenerate levels. The resonance amplitudes exhibit a strong dependence on the type of model used (with or without the inclusion of the degeneration of levels) and on the polarization of light waves. At the same time, the shape of the resonances that is normalized to unit amplitude from which the velocity distribution of atoms can be reconstructed is much less sensitive to the model type.
The problem of the statistics of photoemission events in a specified direction and with a given polarization is solved for a resonantly fluorescing atom with degenerate levels. The degeneracy of the levels is taken into account within the semiclassical approach to the description of the atomic angular momentum. Relationships for the probability distribution of photoemission events in a specified solid angle and with a given helicity are derived for all components of the resonance fluorescence triplet. The results obtained make it possible to elucidate the influence of the polarization of a pump field on the statistics and correlations of photoemission events of different types.
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.
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.
A method has been developed for obtaining the steady-state solution of a quantum kinetic equation for the atomic density matrix in an arbitrarily polarized monochromatic field with the complete inclusion of recoil effects and degeneracy of atomic levels in the projection of the angular momentum. This method makes it possible to obtain the most general solution beyond the previously accepted approximations (semiclassical approximation, secular approximation, etc.). In particular, it has been shown that the laser cooling temperature is a function of not only the depth of the optical potential (as was previously thought), but also the mass of an atom.