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Journal de physique

Collisional transfer of coherence by electric dipole-dipole interaction

W. Gough

Published Jan 1, 1983• 0 citations
Publisher

Abstract

An expression is derived for the contribution from dipole-dipole interaction to the intensity of sensitized fluorescence, from the results of a theory by Chiu. Tensor operator methods are used. The degree of polarization is deduced for certain particular cases.
DOI
10.1051/jphys:01983004403034300

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The polarization of the resonance fluorescence of interacting atoms and the transfer of coherence, due to the exchange of excitation, are studied theoretically. The treatment is for the general case where both the excited and the ground states can have arbitrary angular momenta, except that they can be connected to each other by an allowed transition. Electrostatic dipole–dipole interaction and electromagnetic radiative interaction are considered simultaneously as the perturbations on the system. Heitler and Ma's generalized time-dependent perturbation method is used. The system is quantized with respect to the space-fixed z axis and a static magnetic field along the z axis may be present, so that the magnetic sublevels (m, m′, etc., for the excited state J, and α, β, etc., for the ground state J′) are not necessarily degenerate. The intensity of the scattered light of a given polarization, in a given direction, is expressed as a function of kR (where ℏck is the energy of excitation and R is the internuclear distance), and of the orientation of R with respect to z axis. The matrix elements (ℏ / 2)γmβ,αm′ and Vmβ,αm′, which cause resonant transfer of excitation between two atoms through radiative and electrostatic interaction, respectively, are also expressed as a function of kR, and of the orientation of R. For randomly oriented atoms, the polarization after being averaged over the random orientation of R becomes a function of kR. Numerical calculations have been carried out for S01 → 1P1 transition. The coherence is shown to be conserved upon resonant transfer of excitation when R is parallel to the quantization axis.
By means of the selection rule Σ m J = constant along the axis of a collision between two atoms, it is shown that sensitized fluorescence should in some cases be partially polarized. The degree of polarization of the fluorescence of cadmium vapour sensitized by the presence of mercury vapour is calculated for certain states of polarization of the incident radiation. In the case studied experimentally the degree of polarization varies over a range of 2-5%. The theoretical value is 3/11, which is reduced in practice by various depolarizing effects. The possibility of transfer coherence between eigenstates from mercury to cadmium during a collision is considered.
Excitation transfer is studied theoretically as an integral part of sensitized fluorescence, which is a third order time-dependent process, namely the excitation of the absorber atom, followed by the transfer of excitation from this atom to the receiver atom and finally the emission of sensitized fluorescence from the receiver atom. The phase correlation transmitted through such a third order process gives rise to the angular distribution of sensitized fluorescence which is shown to depend on the fine structure levels of both atoms. Long range electric dipole-dipole interaction is used as the mechanism for excitation transfer. Plane wave motion is assumed for the relative motion between two interacting atoms. A general formula is derived for the relative intensities (hence relative cross sections) of the sensitized fluorescence, involving different sets of fine structure levels. This cross-section ratio turns out to be angular dependent but nevertheless is shown to be expressible in a very simple form which can be readily calculated. The ratio calculation is illustrated for the case of K*(42P1/2,3/2) +Rb(52P1/2,3/2). Nuclear spin effect is also considered. For the weak coupling case, the nuclear spin is found to have no effect on the sensitized fluorescence.