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Physical Review A

Collisional Transfer of Coherence: Polarization of Sensitized Fluorescence

Lue‐Yung Chow Chiu

Published May 1, 1972• 6 citations
Publisher

Abstract

Energy transfer and coherence transfer between two atoms of different species are studied theoretically. The electric dipole-dipole interaction is the mechanism considered for the excitation transfer. A generalized perturbation method for a damping system is used. A general formula is derived for the polarization of the sensitized fluorescence resulting from the excitation transfer. This polarization is shown to be dependent on the angular momenta of the two atoms, and to be independent of their relative velocity as well as of their difference in the energy of excitation. The polarizations are found to be nonzero in many cases which demonstrate the transfer of coherence through collision processes. A general and compact formula is also derived for the polarization of pure fluorescence where excitation exchange has not taken place. The polarization of the sensitized fluorescence is in general smaller than that of the pure fluorescence. This means that the coherence is transferred only partially. Finally, the magnetic field effect has been included. This field depolarization depends on the ${g}_{j}$ values and the lifetimes of the excited states of both atoms. The general feature of the field dependence also differs considerably from that of the Hanle effect for resonance fluorescence.

DOI
10.1103/physreva.5.2053

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Canadian Journal of Physics•Dec 15, 1970•11 citations
Energy transfer and coherence transfer between two atoms of different species are studied theoretically. The electric dipole-dipole interaction is the mechanism considered for the excitation transfer. A generalized perturbation method for a damping system is used. A general formula is derived for the polarization of the sensitized fluorescence resulting from the excitation transfer. This polarization is shown to be dependent on the angular momenta of the two atoms, and to be independent of their relative velocity as well as of their difference in the energy of excitation. The polarizations are found to be nonzero in many cases which demonstrate the transfer of coherence through collision processes. A general and compact formula is also derived for the polarization of pure fluorescence where excitation exchange has not taken place. The polarization of the sensitized fluorescence is in general smaller than that of the pure fluorescence. This means that the coherence is transferred only partially. Finally, the magnetic field effect has been included. This field depolarization depends on the gj{g}_{j}gj​ values and the lifetimes of the excited states of both atoms. The general feature of the field dependence also differs considerably from that of the Hanle effect for resonance fluorescence.
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.
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.
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.
The polarization properties of excited alkali atoms having suffered half collisions with noble gas atoms following excitation by nonresonant photon absorption during a strong collision, are investigated. On the basis of a semiclassical perturbation treatment of the density matrix up to second order in the driving field a general expression for the polarization dependent intensity of the emitted alkali fluorescence is derived. Assuming quasistatic excitation of the collision complex and considering reorientation of the orbital and spin electronic angular momenta within a cut off radius, explicit results for the polarization degrees are presented and discussed, depending on the initial molecular excited state and coupling case.
The Hanle effect, which is commonly exhibited by atoms that emit resonance fluorescence while in a magnetic field, has been observed in sensitized fluorescence of sodium vapor. The sodium atoms were excited by σ+ polarized D1 radiation which produced a vector polarization in the 32P1/2 state, and were then transferred to the 32P3/2 state by collisions with helium atoms. The fluorescence was observed at an angle of 325° to the direction of excitation, and the magnetic field was perpendicular to the directions of the exciting and fluorescent light beams. The addition of helium resulted in the appearance of a circularly polarized D2 component in the fluorescent light. The polarization of the sensitized fluorescence decreased with increasing field as in the ordinary Hanle effect but the width of the Hanle signal was smaller than that observed in resonance fluorescence. The observed narrowing effect is in good agreement with theoretical predictions.