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Optics and Spectroscopy

Manifestation of anisotropic collisional generation of higher polarization moments in polarization of quadrupole emission

V. N. Rebane, T. K. Rebane

Published Jun 1, 2000• 0 citations
Publisher

Abstract

Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.

DOI
10.1134/1.626883

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Cambridge University Press eBooks•Mar 30, 1995•0 citations
Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.
The induction of higher polarization moments-the octupole orientation and the hexadecapole alignment—in the case of two-step excitation of atoms through dipole transitions and their manifestation in the polarization of dipole emission under conditions of anisotropic collisions are studied. For all channels of the two-step excitation process J 0→J 1 J, the efficiencies of production of higher polarization moments with integer and half-integer angular momenta from J=2 to J=7 through the absorption of linearly or circularly polarized light are calculated. The rates of collisional relaxation and interconversion of higher polarization moments, for both orientation and alignment, as functions of frequency detuning of the laser line from the center of the Doppler profile are calculated. The theory is illustrated by an example of two channels of excitation of the atomic state J=2 by circularly polarized light: J 0=0→J 1=1J=2 and J 0=3→J 1=2 (or 3)→J=2. In the first case, the octupole orientation enhances or attenuates the signal of circular polarization depending on the laser frequency detuning. In the second case, it represents the only source producing orientation and circular polarization of the emitted light.
The linear polarization of quadrupole emission by the J=2-J 0=0 transition under conditions of laser excitation in a gas medium is studied. Cases of excitation through dipole and quadrupole absorption of monochromatic laser radiation are considered. Taking into account the anisotropy of collisional relaxation, the contributions of polarization moments of the second and fourth ranks, i.e., those with usual and hexadecapole alignments, to the signal of linear polarization of quadrupole emission are calculated. The dependence of this signal on the laser frequency, the density of the gas medium, and the angles determining the orientation of the system of axes of observation of light polarization relative to a laser ray is studied. The numerical calculations of contributions of usual and hexadecapole alignment to the signal of linear polarization are made for the magnetic quadrupole transition J=2-J 0=0 between the states 2p 5(2 P 1 2/0 )3p′[3/2]2 and 2p 5(2 P 1 2/0 )3s 3s′[1/2]0 of neon atoms in the xenon atmosphere.
A comparative study of the beats of circular polarization generated by anisotropic atomic collisions is carried out on the basis of theoretical calculations for the states J =1, 3/2, and 2 of neon atoms and ions excited by monochromatic laser radiation in xenon atmosphere. Contributions made by ordinary alignment and higher polarization moments (octupole orientation and dodecapole alignment) in the collisional generation of orientation and the signal of beatings of circular polarization are compared.
The contributions of the relaxation of electronic polarization moments of various orders κ to the probabilities for the population transfer between the hyperfine-structure levels of an atom under the action of collisions are studied. It is shown that the contributions of higher electronic polarization moments with κ > 2 are comparable with the contributions of the orientation (κ=1) and the alignment (κ=2) or even exceed them in magnitude. This opens up the possibility of studying the collisional relaxation of higher polarization moments which are usually not observed and not involved in the emission and absorption of light under dipole transitions. The bounds for the allowable values of the rate constants for the collisional relaxation of higher polarization moments are obtained from the condition for nonnegativity of the total probabilities of population transfer between different hyperfine-structure levels under the action of collisions.
Anisotropy of angular momenta: ideas and methods The fundamental idea forming the basis of early quantum theory was the quantization of the angular momentum of the atom, which, at a later stage, assumed the form of the Bohr–Sommerfeld quantization rule [360], namely ∲ pdq = n ℏ where p and q are the generalized momentum and coordinate. This concept has retained its physical meaning in modern-day quantum mechanics [371, 372]. In the course of the further development of quantum mechanical concepts it became increasingly clear that in the theory of atoms and molecules the angular momentum is a ‘dominant’ notion, the fundamental significance of which is in no small degree connected with its dimension of action, which coincides with that of Planck's constant ℏ. In the interaction between particles and a directed beam of photons the angular momentum of the system is conserved, thus forming the basis for the optical method of producing spatial anisotropy of the distribution of the angular momenta of the ensemble of particles, i.e. its optical polarization . In terms of quantum concepts, spatial anisotropy means that in an ensemble of particles a non-equilibrium population of magnetic sublevels m j of angular momenta is created. We make a distinction between the alignment of momenta, for instance in the absorption of linear polarized light, when there is no difference between the population of ± m j -sublevels, and orientation , when such a difference exists. Anisotropic distribution of angular momenta in an excited state, as produced in absorption, manifests itself directly in the polarization of fluorescence. It is rather likely that understanding of the anisotropic distribution of the angular momenta of atoms was enhanced by Hanle's [184] discovery in 1924.