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Physical Review A

Coherence effects in radiatively assisted inelastic collisions: General theory

P. R. Berman

Published Nov 1, 1980• 29 citations
Publisher

Abstract

A radiatively assisted inelastic collision (RAIC) is one in which two atoms collide in the presence of a radiation field to produce a reaction of the form ${A}^{*}+B+\ensuremath{\hbar}\ensuremath{\Omega}\ensuremath{\rightarrow}A+{B}^{*}$. In this paper, a general theory of RAIC is developed with special attention given to the final-state coherences produced by RAIC. These final-state coherences can be monitored by standard experimental techniques (polarization of fluorescence, quantum beats), enabling one to use such studies to gain information on the interatomic potentials that are relevant to the RAIC under consideration.

DOI
10.1103/physreva.22.1838

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Canadian Journal of Physics•Jun 1, 1981•12 citations
A radiatively assisted inelastic collision (RAIC) is one in which two atoms collide in the presence of a radiation field to produce a reaction of the form A∗+B+\ensuremathℏ\ensuremathΩ\ensuremath→A+B∗{A}^{*}+B+\ensuremath{\hbar}\ensuremath{\Omega}\ensuremath{\rightarrow}A+{B}^{*}A∗+B+\ensuremathℏ\ensuremathΩ\ensuremath→A+B∗. In this paper, a general theory of RAIC is developed with special attention given to the final-state coherences produced by RAIC. These final-state coherences can be monitored by standard experimental techniques (polarization of fluorescence, quantum beats), enabling one to use such studies to gain information on the interatomic potentials that are relevant to the RAIC under consideration.
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.
In a previous paper [P. R. Berman and E. Giacobino, Phys. Rev. A 28, 2900 (1983)], a method was proposed for producing electronic-state coherences using radiatively-aided inelastic collisions (RAIC). Two atoms collide in the presence of two simultaneously applied laser pulses and the combined action of the fields and the collision leads to a final-state coherence ${\ensuremath{\rho}}_{\mathrm{ij}}$ between levels iii and jjj in one of the atoms. In this paper a detailed calculation of the RAIC cross section is given, including effects of magnetic degeneracy and an average over all collision orientations. With an isotropic distribution of collision orientations and with one photon absorbed from each laser field in a single RAIC reaction, a final-state coherence ${\ensuremath{\rho}}_{\mathrm{ij}}$ is created only if states iii and jjj have the same parity. In order to produce a final-state coherence between states of opposite parity, an anisotropic distribution of collision orientations is needed. Estimates of RAIC cross sections are obtained for both isotropic and axially symmetric distributions of collision orientations. For final states having opposite parity, the RAIC reaction can lead to the production of coherent radiation at the sum or difference frequency of the applied laser fields.
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.
Recently, a theoretical calculation has been presented assuming that coherences can be produced in a radiatively assisted inelastic collision. The author reports the observation of final-state coherences in the simple case of dipole-dipole interaction in a strontium-europium mixture illuminated by a pi -polarised laser field. The author has measured the polarisation ratio P of the fluorescence emitted from the final degenerate Zeeman states of strontium. The result P=0.43+or-0.05 is in good agreement with theoretical predictions P=0.45.
A theory is given of radiative collisions, i.e., of elementary events in which the emission of a photon occurs in the course of a collision. Special attention is paid to radiative collisions stimulated by a laser field. Simple but clear approaches formulated in the forties or fifties are described briefly. This theory applies, in particular, to collisions in a strong electromagnetic field which affect the collision dynamics. Chemical radiative collisions, i.e., chemical reactions stimulated by photons absorbed in the course of a collision, are reviewed. An analysis is made of several recent experiments in which the theoretically predicted effects were observed: these include the radiative-collisional transfer of excitation from atom to atom, nonlinear effects due to the influence of the field on the collision dynamics, and photosubstitution of one of the atoms in a halogen molecule with an inert gas atom.
A theory of resonant light scattering from two level atoms in a gas is developed for an arbitrarily strong pump field. The Doppler effect and two body foreign gas collisions are considered. Elastic, inelastic (upward and downward), and the velocity changing collisions are retained in the general formulation. The impact approximation is not made, and the expressions for all (field dependent) collision rates are generated internally. Particular attention is paid to the lower state interaction, and a more complete parameterization of the theory is achieved. The general theory is non-Markovian and the quantum regression theorem is not used; it reduces to existing theories in special cases. It is shown that the coherent scattering is not a general property of the system if the lower state interaction is present; the "coherent" component acquires a small, but nonzero, width in the strong field region. This width could provide information about some new collision parameters.