The role of collision-induced transfer of electronic state coherence on the spectral response of an atomic vapor is investigated. It is shown that such collisional effects can lead to the appearance of narrow resonances in the nonlinear spectroscopy of three-level systems. Collisional transfer between different multipoles of electronic state coherence is shown to lead to a breakdown of several percent in Becquerel's relation between the Faraday rotation and dispersion of a vapor. All calculations are carried out in the impact limit of pressure broadening theory. Particular emphasis is given to the order in which the various averages over the velocity distributions of both the active atoms and perturbers must be performed. In particular, for the effects described herein, the various collisional transfer rates vanish when averaged over the active atom velocity distribution. It is essential, therefore, to obtain the final line-shape formulas, including velocity-dependent collisional transfer rates, before carrying out the average over the active atom velocity distribution. The experimental observation of these spectral features would provide direct evidence for the existence of these collisional transfer processes.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
Collisional processes occurring within an atomic vapor can be conveniently described in terms of collision kernels. The population kernel ${W}_{\mathrm{ii}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ gives the probability density per unit time that an "active" atom in state
i undergoes a collision with a perturber that changes the active atom's velocity from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}$ to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. For active atoms in a linear superposition of states
i and
j, there is an analogous coherence kernel ${W}_{\mathrm{ij}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}) (i\ensuremath{\ne}j)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\ensuremath{\rho}}_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states
i and
j differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states
i and
j. Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.
A general theory of atomic dipole coherence under the influence of collisional phase changes, inelastic effects and optically active atom velocity changes, including those due to anisotropic interactions is presented. Velocity change effects are obtained in closed form. Line shapes appear as convolutions of standard pressure broadening contours with velocity-change contours. Width and shift parameters for the He-broadened Na D lines at 2 m bar pressure, 380 K are calculated, as are He-induced photon echo decay rates for these lines. Overall agreement with xperiment is reasonably good.
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 the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.
A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.