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Physical Review A

Quantized-field approach to pressure-induced resonances

P. R. Berman, G. Grynberg

Published Dec 1, 1989• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.40.6921

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Physical Review A•Mar 1, 1990•29 citations
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.
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.
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.
In the experiment with barium vapor (close approximation of a two-level system) we found spectra of resonance fluorescence having the form of a pressure-broadened line with a narrow, not collisionally broadened, dip. They are interpreted as the result of collisionally-induced quantum interference among possible spontaneous emission channels of a dressed atom subjected to stochastic perturbation. Also, the analogy between these effects and the coherent population trapping in three-level systems is pointed out.
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 theory of four-wave mixing is developed using an amplitude approach in the Schr\"odinger picture. It is shown that the four-wave mixing signal produced when three fields are incident on an ensemble of two-level atoms can be viewed as arising from constructive interference of the signals emitted at the various atomic sites. Fourteen distinct amplitudes contribute to the four-wave mixing signal. Some of these amplitudes involve final states in which one or two atoms are excited, and some involve final states in which photons are emitted into modes other than a phase-matched mode of interest. The amplitude approach has the advantage of clearly showing the atom-field correlations. It helps one to understand the underlying physical mechanisms responsible for creation of the four-wave mixing signal, as well as features in the line shape resulting from collisions and effects relating to atomic recoil on the absorption or emission of radiation. These so-called collision- and recoil-induced resonances are calculated explicitly using the amplitude approach, and an interpretation of the results in terms of the interference between different amplitudes is given. Our results, calculated for a finite interaction time between the atoms and the fields, are compared with analogous calculations in which an effective ground-state decay time is assumed. It is shown that the results differ if the atom-field interaction time is not the longest relevant time parameter in the problem.
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.