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Journal of Physics B Atomic and Molecular Physics

Resonances between 'unpopulated levels' in non-linear optics

G. Grynberg

Published Jun 28, 1981• 54 citations
Publisher

Abstract

Documenting (1977) and Bloembergen (1979) have suggested that resonances between unpopulated levels should be observed in non-linear optics. Using the theory of the dressed atom, the author shows that these resonances correspond to the pumping of a coherence of the dressed atom because of the collisions. He shows that these resonances are closely related to the collisional redistribution of radiation. Finally, he shows that these resonances can generally be observed only in the frequency range where the impact approximation can be applied.

DOI
10.1088/0022-3700/14/12/020

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Documenting (1977) and Bloembergen (1979) have suggested that resonances between unpopulated levels should be observed in non-linear optics. Using the theory of the dressed atom, the author shows that these resonances correspond to the pumping of a coherence of the dressed atom because of the collisions. He shows that these resonances are closely related to the collisional redistribution of radiation. Finally, he shows that these resonances can generally be observed only in the frequency range where the impact approximation can be applied.
Theory relevant to the treatment of resonance collisions between two-level dressed atoms has been extended to the three-level case in a self-contained calculation of field-dependent collision rates. With the laser field tuned close to the \ensuremath{\Vert}e1{\mathit{e}}_{1}e1​〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}e2{\mathit{e}}_{2}e2​〉 transition, dressing of the upper two-level system is achieved. We solve coupled equations of motion for two-atom states that describe one atom in the ground state and the other in one of two dressed states. Dressed-state collision rates are calculated within the impact approximation using S-matrix theory. The coupled equations of motion are simplified in the limit of intense field. We have applied the theory to describe approximately collisions between Ne atoms in fields intense enough to dress the collision complex.
We extend the theory of light scattering from an atom undergoing collisions to the case of strong laser fields, where the expansion in powers of $\ensuremath{\Omega}{\ensuremath{\tau}}_{c}$ that was used formerly in a series of papers by Burnett et al. breaks down. In particular we consider in detail the conditions necessary to relate the observable quantities to intense-field collisional rate constants in a dressed-state basis (such as those calculated by Light and Sz\"oke). We also show (following Rabin and Ben-Reuven) that by studying the spectrum emitted by the atoms in the presence of a strong field one may measure the collisional rates for transfer between the dressed states of atom plus radiation field.
Résumé. 2014 La description de la fluorescence de résonance par la méthode de l’atome habillé est généralisée pour inclure les effets collisionnels. Ces effets s’interprètent comme une modification par les collisions de la cascade radiative de l’atome habillé. Toutes les caractéristiques des spectres d’absorption et d’émission sont exprimées en fonction des paramètres de relaxation, de type T1 et T2, de l’atome habillé. On analyse le domaine de validité de cette approche et on montre qu’il est plus large que celui des équations de Bloch optiques. Les paramètres de relaxation sont reliés à la matrice S de collision. En utilisant une représentation de spin, on les met également sous la forme de transformées de Fourier d’une fonction de corrélation de la perturbation collisionnelle. Abstract. 2014 The dressed atom approach to resonance fluorescence is extended to include collisional effects. These effects appear as a collision induced modification of the radiative cascade of the dressed atom. All the cha-racteristics of absorption and emission spectra are expressed in terms of the T1 and T2 type relaxation para-meters of the dressed atom. The domain of validity of this approach is investigated and is shown to be larger than that of the optical Bloch equations. The relaxation parameters are related to the collision S matrix. By using a spin representation, they are also expressed in terms of the Fourier transform of some correlation function of the collisional perturbation.
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.
The authors have studied resonance collisions amongst atoms dressed by a strong laser field. The equations of motion have been solved numerically to yield collisional transition rates for various values of the Rabi frequency (V) due to the laser and its detuning ( Delta ) from the atomic transition frequency ( omega 0 ). The atoms are assumed to follow classical rectilinear paths and only undergo binary collisions. The resonance interaction is taken to be the first-order dipole-dipole interaction acting within the ground and resonance levels of a pair of atoms. A qualitative explanation is offered for the results obtained by splitting the Hamiltonian into parts that represent the collision-free evolution of the system at the Rabi frequency, the 'normal' resonance interaction, and the 'dressed interaction' responsible for opening new scattering channels. The latter interaction depends upon the relative strengths of the resonance interaction (R), the generalized Rabi frequency ( Omega ) and the ratio V/ Delta .
Resonant scattering (redistribution) of weak monochromatic light by atoms in the presence of collisions has been considered by Omont et al., who allowed for the broadening of both upper and lower levels of the transition. Mollow (who also has considered this problem for intense radiation) has shown that their results are applicable only if collisional repopulation of the levels (in contrast to collisional depopulation) is ignored. We here consider in detail the effect of repopulation. It leads, in the weak-field limit, to a true-coherent component ($\ensuremath{\delta}$-function spectrum) at the driving frequency, as well as a component at this frequency whose width is essentially the inelastic collisional rate of the lower state. An additional redistributed component due to repopulation of the upper level is also obtained.