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Physical Review A

Theory and interpretation of pressure-induced resonances

P. R. Berman, G. Grynberg

Published Jan 1, 1989• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.39.570

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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.
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.
A theory of four-wave mixing including effects of velocity-changing collisions is presented. Three fields with frequencies \ensuremath{\omega}, \ensuremath{\omega}, and \ensuremath{\omega}+\ensuremath{\delta} are incident on a vapor of ``two-level'' atoms having upper state b and lower state a. Two of the fields are counterpropagating and the third (of frequency \ensuremath{\omega}+\ensuremath{\delta}) makes a small angle with one of the others. The frequency \ensuremath{\omega} is a nearly resonant (inside the Doppler width) with the a-b transition frequency. The phase-conjugate signal emitted at frequency \ensuremath{\omega}-\ensuremath{\delta} is calculated as a function of \ensuremath{\delta}. Using a simple collision model in which collisions are phase interrupting in their effect on atomic coherence and velocity-changing in their effect on level populations, we discuss the conditions under which resonances characterized by the upper or lower radiative and collision rates can be observed. Assuming that the total (a+b) state population is conserved in the absence of collisions, it is shown that velocity-changing collisions can ``open'' the system and lead to a resonance characterized by the lower-state width (convoluted with the residual Doppler width). With increasing pressure, the width of this induced resonance structure decreases monotonically. For sufficiently high pressure, the collisional redistribution of velocity classes is complete---the system ``recloses'' and the narrow resonance disappears. The interplay of the collision-induced opening, line narrowing, and reclosing of the system is discussed, as is the relationship of these narrow resonances to the so-called pressure-induced extra resonances of Bloembergen and co-workers [Indian J. Pure Appl. Phys. 16, 151 (1978); Phys. Rev. Lett. 46, 111 (1981)].
A method for producing electronic-state coherences using either collisionally-aided radiative excitation (or "optical collision") or laser-induced collisional energy transfer (or "radiative collision") is proposed. Two atoms, AAA and ${A}^{\ensuremath{'}}$, collide in the presence of two pulsed-laser fields having frequencies $\ensuremath{\Omega}$ and ${\ensuremath{\Omega}}_{1}$. It is shown that by choosing ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ such that an energy-conserving transition can occur in the composite $A{A}^{\ensuremath{'}}$ system, one can create an electronic-state coherence in the AAA or ${A}^{\ensuremath{'}}$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.
The spectrum of light emitted by a single atom in a thermal bath interacting with three electromagnetic fields is calculated using the dressed-atom picture. The emission spectrum consists of an elastic Raman-like component and dephasing-induced redistribution components that are inelastic in nature. In contrast to coherent four-wave mixing [as given by chi((3))], in which a pressure-induced elastic component (PIER 4) has been predicted and observed, the single-atom response does not contain any elastic pressure-induced components. We derive explicit expressions for the single atom and for the PIER 4 spectra that are not restricted to the impact limit.
A theory of collisionally aided radiative excitation (CARE) for three-level systems in the weak-field limit is presented. Cross sections for the excitation of three-level atoms by two off-resonant pulsed radiation fields in the presence of collisions with structureless perturbers are calculated. Analytic expressions for the cross sections as functions of atom-field detunings are obtained under usual classical-trajectory and rotating-wave approximations using perturbation theory for various regions of detunings. Examples for the resulting excitation line shapes are given mostly for van der Waals potentials. A dressed-atom picture of the CARE processes is discussed. Emphasis is put on an interesting effect arising from the interference between the "stepwise" and the "direct" channel of excitation. Such an interference effect manifests itself as modulations in the total excitation cross section as a function of relative interatomic speed in some cases.