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Physical Review A

Effective two-level description of pressure-induced extra resonances in four-wave mixing

G. S. Agarwal, J. Cooper

Published Nov 1, 1982• 16 citations
Publisher

Abstract

The possibility of formulating a treatment of pressure-induced extra resonances (PIER) in four-wave mixing, in terms of effective two-level equations, is examined. With the use of the method of adiabatic elimination of fast variables, effective two-level equations, which are valid for arbitrary slowly varying field envelopes, are obtained. Such equations are found to have a structure that is very different from that of the Bloch equations. In the new structure important inhomogeneous terms appear that are crucial for PIER. The present description is then used to study the effect of laser fluctuations on PIER.

DOI
10.1103/physreva.26.2761

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The possibility of formulating a treatment of pressure-induced extra resonances (PIER) in four-wave mixing, in terms of effective two-level equations, is examined. With the use of the method of adiabatic elimination of fast variables, effective two-level equations, which are valid for arbitrary slowly varying field envelopes, are obtained. Such equations are found to have a structure that is very different from that of the Bloch equations. In the new structure important inhomogeneous terms appear that are crucial for PIER. The present description is then used to study the effect of laser fluctuations on PIER.
The effect of pump fluctuations on various coherent processes that arise in three-level systems interacting with two external fields is examined. Such coherent processes include the forward Hanle effect and various four-wave mixing effects such as the generation of phase-conjugate signals. A general formulation that enables one to calculate the influence of laser linewidth on the coherent signals produced in various directions is presented. Ensemble averages, over laser temporal fluctuations, of various physical quantities, such as atomic polarization, are calculated. The spectrum of polarization fluctuations is shown to consist of several new features which lead to coherent radiation in different directions depending on the resonant frequencies in the polarization fluctuations. The influence of pump linewidth on pressure-induced extra resonance (PIER) is treated in detail. The possibility of producing a laser-fluctuation-induced coherent signal at one of the atomic frequencies is examined. This new signal, which is produced in a direction different from that of the PIER signal, but has the same type of resonant character as PIER, is found to have significantly different pressure dependence than the PIER signal. The results of our numerical computations are qualitatively explained in terms of the convolutions of products of third-order susceptibilities and pump field-correlation functions.
A nonperturbative density-matrix formalism is used for the analysis of strong-field four-wave mixing, allowing the treatment of relaxation processes, including lifetime as well as dephasing. The combined role of proper dephasing and level saturation in the generation of extra resonances is studied. It is shown that, whereas in the absence of proper dephasing there is no pressure-induced resonance, there is always a nonzero contribution to the field-induced resonance. For increasing field intensity, a characteristic double saturation is predicted as a function of the field strength. The dependence on the various parameters is investigated, and the conditions under which these effects should be observable are identified.
Using both a bare-atom and dressed-atom picture of atom-field interactions, we present a theory of the pressure-induced resonances that can arise when four radiation fields interact with a three-level quantum system. The four fields drive two coupled atomic transitions which share a common level, the levels being arranged in a ``ladder'' scheme. As the field frequencies are varied, certain resonant structures in the excitation spectrum of the upper state population appear only in the presence of collisions. The resonant structures result from processes that have been referred to in the past as collisionally aided radiative excitation (CARE) and pressure-induced extra resonances in four-wave mixing (PIER4). We show that both CARE- and PIER4-type resonances have a common origin, which can be linked to conservation of energy. In contrast to conventional PIER4 signals, line shapes calculated in this work result from a ``single atom'' rather than a collective emission. Moreover, the signals vanish unless the applied fields are relatively coherent, again in contrast to conventional PIER4.
A nonperturbative semiclassical theory is presented for the treatment of four-wave mixing (FWM) in a four-level system. This treatment is based on a transformation to a generalized rotating frame followed by a numerical diagonalization of the resulting time-independent Hamiltonian. For strong fields, all resonant frequencies are shifted from the atomic (molecular) frequencies. Lines are split up in a way similar to the ac Stark effect for a two-level system, and for even stronger fields, the effect of stirring is observed for the first time in four-wave mixing. In addition, a new extra resonance appears which is induced by the saturating field. This field-induced resonance is the new member in the family of extra resonances (pressure induced, or stochastic fluctuation induced), and it should be observed whenever saturating fields interact with a multilevel atomic or molecular system.