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Optics and Spectroscopy

Induction of ordered states of angular momenta in an ensemble of excited particles under the action of a nonuniform magnetic field

Victor L. Kantsyrev, A. G. Petrashen, Alla S. Shlyaptseva

Published Nov 1, 2006• 0 citations
Publisher

Abstract

It is shown that a nonuniform magnetic field can induce ordered states of angular momenta. Concrete calculations are carried out for the magnetic field of a linear current and a field nonuniform in the plane of observation of polarized radiation.
DOI
10.1134/s0030400x06110014

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We know now how alignment and orientation of angular momenta arise in the excited state as a result of optical excitation from the primarily isotropic distribution of the ensemble of angular momenta. This phenomenon reflects, in essence, the anisotropy of absorption probability G (θ,ϕ). Since spatial structures of the type shown in Fig. 2.2 appear in the excited state the same structure must be ‘eaten out’ from the angular momentum distribution in the ground (initial) state. If the gap created is not closed quickly enough, the ensemble of the remaining angular momenta of the absorbing molecules in the ground state must necessarily also be polarized. If, from another point of view, fluorescent decay leads to a considerable population of the ground state level c, (see, e.g., Fig. 1.2), then molecules on this level may exhibit angular momenta polarization, being particularly noticeable for thermally unpopulated, high lying levels. In the present chapter we intend to discuss the conditions necessary for the creation of ground state angular momenta polarization, the possibilities of its experimental observation, and to develop the theoretical description of broad line radiation interaction with molecules further. Angular momenta polarization via depopulation For many years there existed the widespread opinion that in molecules we obtain an anisotropic distribution of angular momenta only in the excited state in the absorption process, whilst in the ground state isotropy is conserved [124]. This conjecture is based essentially on the assumption of the existence of a so-called ‘weak’ excitation. At first sight it may appear, for instance, from Eq. (2.20) that, as is usual in non-linear spectroscopy, such an admission is correct if condition Γ p /Γ ≫ 1 is valid.
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 Wigner representation of angular-momentum orientation in the classical limit on $J\ensuremath{\gg}1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\stackrel{\ensuremath{\rightarrow}}{J}J$ or $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, 1/J,1/\sqrt{J},1/J​, of the angular-momentum orientation. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ or $\stackrel{\ensuremath{\rightarrow}}{J}J,$ transition particles come into ``dark'' states while for the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition they occupy the ``brightest'' state. In the presence of a nonzero magnetic field, particles with $\stackrel{\ensuremath{\rightarrow}}{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition the directions of the angular momentum form a cone around the magnetic field.