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Physical Review A

Spectra of four-wave mixing in a self-consistent field

Gautam Gangopadhyay, Deb Shankar Ray

Published Apr 1, 1990• 0 citations
Publisher

Abstract

We have presented a semiclassical analysis of four-wave mixing in a system of two-level atoms interacting with a single-mode self-consistent classical electromagnetic field in the presence of a weak probe field. The relevant response functions for the probe wave as well as for the field generated by the four-wave mixing have been calculated over a wide-range coupling constant for the self-consistent field and the atoms. The significant departures from the spectral characteristics associated with the usual four-wave mixing with an external strong pump field arise. The probe wave and the four-wave mixing spectra have been interpreted in terms of simple excitation transfer in the atom--self-consistent-field coupled oscillator model.

DOI
10.1103/physreva.41.3985

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We have presented a semiclassical analysis of four-wave mixing in a system of two-level atoms interacting with a single-mode self-consistent classical electromagnetic field in the presence of a weak probe field. The relevant response functions for the probe wave as well as for the field generated by the four-wave mixing have been calculated over a wide-range coupling constant for the self-consistent field and the atoms. The significant departures from the spectral characteristics associated with the usual four-wave mixing with an external strong pump field arise. The probe wave and the four-wave mixing spectra have been interpreted in terms of simple excitation transfer in the atom--self-consistent-field coupled oscillator model.
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Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave mixing, population modulation, and Zeeman optical pumping are derived. On all these observables, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the D2{D}_{2}D2​ line of Rb vapor are presented in good agreement with the calculations.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations
In this paper we analyze theoretically the influence of the local-field effects on reflection spectra of a degenerate four-wave mixing in a dense medium of two-level atoms. We discuss the spectral dependence of the nonlinear absorption and dispersion of the signal and probe fields as well as their coupling for various strengths of the external field and atomic densities. For weak external fields the local-field effects reduce to the well known Lorentz redshift of the reflection spectra. When the external field saturates the transition in a dense sample significant modifications of the probe reflectivity and of the wave mixing spectra occur, resulting in asymmetric, multipeak line shapes. \textcopyright{} 1996 The American Physical Society.
A very large number of physical phenomena in the resonant interaction of atomic-molecular systems with the radiation fields can be studied by treating the atomic system as a two level system and by examining its response to the applied fields. Various perturbative results are well known. A number of recent experimental works require the knowledge of the nonperturbative response functions, when both the applied fields are strong. These include a variety of experiments on instabilities(1) in lasers involving the switching from a single mode to for example two mode operation. Similarly recent nonlinear mixing experiments, where not only four wave mixing but also higher mixing in saturating fields has been studied. Pump probe experiments have also been repeated with probes whose intensity could be large. The purpose of this paper is to formulate the general theory and use it to understand the experiments. The formulation we present is also well suited for studying the effect of collisions. Details of various collisional induced coherences in fourwave and six wave mixing etc. can be studied.