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Physical Review A

Pressure-induced effects in two-level atoms: New approach and simple physical interpretation

G. Grynberg, P. R. Berman

Published Apr 1, 1989• 22 citations
Publisher

Abstract

Pressure-induced effects in nonlinear optics and spectroscopy are studied using a nonstandard-dressed-atom formalism for a set of two-level atoms. We consider a two-level atom interacting with two radiation fields whose frequencies differ by \ensuremath{\delta} and undergoing dephasing collisions with a perturber bath. The atom-field detunings are large compared with all relaxation rates in the problem. The system is described by a Hamiltonian of an atom dressed by a single-mode field with a coupling constant slowly varying in time at frequency \ensuremath{\delta}. We show that the collisionally aided excitation of the initially unpopulated dressed states is modulated in time. All the characteristics of the pressure-induced effects are deduced from the properties of this time-modulated excitation. Apart from already known phenomena (pressure-induced extra resonances in four-wave mixing, pressure-induced phase shifts, etc.) that are reinterpreted using this approach, we present a new effect that can be described as fluorescence beats. Finally, we show that this approach gives a firm basis for use of a model involving collision-induced gratings and we interpret the pressure-induced effects in the context of this model.

DOI
10.1103/physreva.39.4016

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Pressure-induced effects in nonlinear optics and spectroscopy are studied using a nonstandard-dressed-atom formalism for a set of two-level atoms. We consider a two-level atom interacting with two radiation fields whose frequencies differ by \ensuremath{\delta} and undergoing dephasing collisions with a perturber bath. The atom-field detunings are large compared with all relaxation rates in the problem. The system is described by a Hamiltonian of an atom dressed by a single-mode field with a coupling constant slowly varying in time at frequency \ensuremath{\delta}. We show that the collisionally aided excitation of the initially unpopulated dressed states is modulated in time. All the characteristics of the pressure-induced effects are deduced from the properties of this time-modulated excitation. Apart from already known phenomena (pressure-induced extra resonances in four-wave mixing, pressure-induced phase shifts, etc.) that are reinterpreted using this approach, we present a new effect that can be described as fluorescence beats. Finally, we show that this approach gives a firm basis for use of a model involving collision-induced gratings and we interpret the pressure-induced effects in the context of this model.
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.
Using a fully quantized dressed-atom approach, we present a theory and interpretation of the pressure-induced resonances in four-wave mixing (PIER4) that may arise when three incident fields interact with an ensemble of two-level atoms. The PIER4 resonances are seen to arise from a collisionally created modulation of a dressed-state population when an operator approach is used to solve the problem and from a level crossing between collisionally populated dressed states when an occupation-number formalism is used.
We present three examples of pressure-induced extra resonances that can be observed in nonlinear spectroscopy: fluorescence of a ``three-level atom'' driven by two laser fields, two-photon ionization of a ``three-level atom'' (plus continuum) driven by two laser fields, and excitation of a ``four-level atom'' driven by four laser fields. We show that all these extra resonances can be interpreted in terms of quantum pathways, each pathway involving a collisionally aided excitation. We also demonstrate that the two first extra resonances can be obtained with incoherent fields, while relatively coherent fields are required in the last example.
Collisional perturbation of atoms in a vapor is well known to induce additional resonances in degenerate or nearly degenerate four-wave mixing.1,2 Actually the effect of collisions in nonlinear optics includes a much broader class of phenomenon, in which the dephasing of the wave functions during the collisions modifies the response of the medium to the input waves. Two examples of such effects are described: coherent emission of radiation induced by collisions and collisionally aided amplification.
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.