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Physical Review A

Generation of magnetic-state polarization in light-induced collisional energy transfer: Weak-field, quasistatic-wing limit

P. R. Berman, F. Schuller, Gerard Nienhuis

Published Jul 1, 1990• 9 citations
Publisher

Abstract

A reaction of the form Ai+Ai\ensuremath{'}\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}Af+Af\ensuremath{'}\ensuremath{'} has been referred to as light-induced collisional energy transfer (LICET). In such a reaction, atoms A and A\ensuremath{'} collide in the presence of a radiation field and absorb a photon during the collision, taking them from initial states (Ai,Ai\ensuremath{'}\ensuremath{'}) to different final states (Af,Af\ensuremath{'}\ensuremath{'}). We calculate the final-state magnetic polarization produced in LICET for detunings \ensuremath{\Delta}=[(Ef+Ef\ensuremath{'})-(Ei+Ei\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega})]/\ensuremath{\Elzxh} in the quasistatic wing: that is, for |\ensuremath{\Delta}|\ensuremath{\tau}c\ensuremath{\gg}1, where \ensuremath{\tau}c is the collision duration. Our results are compared with analogous depolarization rates for so-called ``optical'' collisions (reactions of the form Ai+Ai\ensuremath{'}\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}Ai+Af\ensuremath{'}\ensuremath{'}). Similarities and differences between the LICET and ``optical'' collision theories are noted. Final-state LICET magnetic-state polarization is evaluated for a number of different A-A\ensuremath{'} level schemes, assuming a dipole-dipole collisional interaction. Our results are shown to be in good agreement with experiment [A. D\'ebarre, J. Phys. B 15, 1693 (1982)].

DOI
10.1103/physreva.42.459

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A reaction of the form Ai+Ai\ensuremath{'}\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}Af+Af\ensuremath{'}\ensuremath{'} has been referred to as light-induced collisional energy transfer (LICET). In such a reaction, atoms A and A\ensuremath{'} collide in the presence of a radiation field and absorb a photon during the collision, taking them from initial states (Ai,Ai\ensuremath{'}\ensuremath{'}) to different final states (Af,Af\ensuremath{'}\ensuremath{'}). We calculate the final-state magnetic polarization produced in LICET for detunings \ensuremath{\Delta}=[(Ef+Ef\ensuremath{'})-(Ei+Ei\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega})]/\ensuremath{\Elzxh} in the quasistatic wing: that is, for |\ensuremath{\Delta}|\ensuremath{\tau}c\ensuremath{\gg}1, where \ensuremath{\tau}c is the collision duration. Our results are compared with analogous depolarization rates for so-called optical'' collisions (reactions of the form Ai+Ai\ensuremath{'}\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}Ai+Af\ensuremath{'}\ensuremath{'}). Similarities and differences between the LICET and optical'' collision theories are noted. Final-state LICET magnetic-state polarization is evaluated for a number of different A-A\ensuremath{'} level schemes, assuming a dipole-dipole collisional interaction. Our results are shown to be in good agreement with experiment [A. D'ebarre, J. Phys. B 15, 1693 (1982)].
The behavior of the quasistatic wing of the light-induced collisional-energy-transfer (LICET) line shape is analyzed. The reaction can be written as A∗{A}^{\mathrm{*}}A∗+B+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}A+B∗∗{B}^{\mathrm{*}\mathrm{*}}B∗∗. The two-level model is found to be inadequate to describe the falloff of the spectral line shape in the quasistatic wing. The three-level model, on the other hand, leads to the prediction of a cross section that depends on the detuning in various ways, according to the strength of the collisional coupling and the influence of the van der Waals shifts on the levels under consideration. Good agreement with existing experimental results is found. To check the approximations made in the derivation of these results, numerical evaluation of the transition probability has been performed for several cases. A Monte Carlo simulation of the full LICET spectrum is also presented.
We examine theoretically the behavior of cross sections for laser-induced collisional energy transfer (LICET) over a wide range of detunings and laser intensities for the two-atom pairs Li-Sr and Eu-Sr which have been previously studied experimentally. These two cases are complementary in that the laser and collisional interactions enter in opposite orders, and their level structures are such as to give weak-field line shapes of opposite asymmetry and intensity shift. A three-state model is used and the Bambini-Berman formula for the weak-field quasistatic wing is verified. At high intensities the peak cross section is found to go through a maximum and the LICET profile is found to become symmetric about a shifted center with notable departures from a uniform falloff in the far quasistatic wing, apparently arising from radiative collisional interference effects.
It is shown that the conventional two-state theory of laser-induced collisional energy transfer (LICET) cannot be expected to provide an adequate description of the quasistatic wing behavior observed in a number of high-resolution LICET experiments. The theory breaks down whenever the detuning parameter \ensuremath{\Delta} of the LICET reaction is comparable to some frequency mismatch \ensuremath{\delta}\ensuremath{\omega} between either the initial or final state and a (virtual) intermediate state in the reaction. A simple extension of the conventional two-state theory is presented which leads to good agreement with experiment. For a van der Waals collisional interaction, the quasistatic wing is shown to fall off as \ensuremath{\Vert}\ensuremath{\Delta}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/2}$(\ensuremath{\delta}\ensuremath{\omega}+\ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}${)}^{\mathrm{\ensuremath{-}}3/2}$ instead of \ensuremath{\Vert}\ensuremath{\Delta}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/2}$ predicted by the two-state theory.
The theory of light-induced collisional energy transfer (LICET) in the Eu-Sr system is extended to include all the degenerate M states that occur in the separated-atom basis states. Previous treatments were restricted to only the M=0 substates. Numerical solutions are obtained for the resulting nine-state dynamic coupled system to determine transitions probabilities on a given straight-line path. Intense laser fields of linear and circular polarization are treated. It is found that the full M-state treatment results in dependences on the trajectory orientation angles which are much more complex than in the M=0 treatment. The exact and quasisymmetries involving these orientation angles are described in simple group-theoretic terms. The resulting spectral line shapes (LICET transition cross sections as a function of laser detuning) are seen to have structures that are understood in terms of the coupling matrix elements, as well as appreciable Stark shifts. These shifts, which appear to be an essential outcome of the theory, are not yet seen in measurements of the LICET line shape.
A fully quantum treatment of the laser induced collisional energy transfer (LICET) processes, , where n = 3,4, is presented, which allows for non-adiabatic mixing between molecular states during the collision. LICET profiles have been calculated for both Lennard-Jones 12 - 6 and model adiabatic molecular potentials. The weak field LICET profiles obtained differ from those of conventional mixed metal vapour systems in that they are very broad, significantly shifted from zero detuning and exhibit novel complex resonant structure in the quasistatic wing. The profiles are very sensitive to the nature of the molecular potential at internuclear separations of less than and consequently differ greatly for the two sets of potentials used.
A theoretical calculation of the final-state coherences produced by a radiatively assisted inelastic collision (RAIC) is presented. Two atoms, AAA and ${A}^{\ensuremath{'}}$, collide in the presence of an external radiation field to produce the RAIC reaction ${A}_{i}+{A}_{{i}^{\ensuremath{'}}}^{\ensuremath{'}}+\ensuremath{\hbar}\ensuremath{\Omega}\ensuremath{\rightarrow}{A}_{f}+{A}_{f}^{\ensuremath{'}}$, where $|{\mathrm{ii}}^{\ensuremath{'}}〉$ is the initial state, $|{\mathrm{ff}}^{\ensuremath{'}}〉$ is the final state, and $\ensuremath{\Omega}$ is the frequency of the external field. It is assumed that the final states consist of a number of nearly degenerate levels and the coherences produced in these levels by the RAIC reaction is calculated. These final-state coherences can be monitored by standard techniques (polarization of fluorescence, quantum beats) enabling one to use the final-state coherences as a probe of the RAIC reaction. The calculation is limited to the weak-field (perturbation-theory) limit and is valid only in the impact core of the RAIC profile.