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Journal of Physics B Atomic and Molecular Physics

Optical emission by spin-polarised atoms

David G. Ellis

Published Aug 21, 1977• 11 citations
Publisher

Abstract

Equations are derived for the polarisation of light emitted by impulsively excited atoms. A spontaneous electric dipole transition between Russell-Saunders terms is considered. The density matrix of the excited term is described by a double tensor expansion which allows for anisotropy in the directional distribution of the spin as well as the orbital angular momentum. Conditions are discussed under which one may test for the presence of spin anisotropy by polarisation measurements or zero-field quantum beats.

DOI
10.1088/0022-3700/10/12/009

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Equations are derived for the polarisation of light emitted by impulsively excited atoms. A spontaneous electric dipole transition between Russell-Saunders terms is considered. The density matrix of the excited term is described by a double tensor expansion which allows for anisotropy in the directional distribution of the spin as well as the orbital angular momentum. Conditions are discussed under which one may test for the presence of spin anisotropy by polarisation measurements or zero-field quantum beats.
Abstract When polarized light is absorbed by an atom, the excited atomic system carries information about the initial polarization of light. For the light that carries an orbital angular momentum, or the twisted light, the polarization states are described by eight independent parameters, as opposed to three Stokes parameters for plane waves. We use a parameterization of the spin-density matrix of the twisted light in terms of vector and tensor polarization, in analogy with massive spin-1 particles, and derive formulae that define atom’s response to specific polarization components of the twisted light. It is shown that for dipole ( S → P ) atomic transitions, the atom’s polarization is in one-to-one correspondence with polarization of the incident light; this relation is violated, however, for the transitions of higher multipolarity ( S → D , S → F , etc) We pay special attention to contributions of the longitudinal electric field into the matrix elements of atomic transitions.
A density-matrix formulation is given of two-photon ionisation of alkali atoms, for two incoming light pulses of arbitrary direction, polarisation, pulse duration and time difference. The frequency of one of the pulses coincides with a resonant transition. The emphasis is on separating out angular momentum factors from the basic physics contained in the radial matrix elements of the atomic electric dipole. The bandwidth of the exciting light is assumed large compared to natural and induced linewidths. The polarisation of the photoelectron is calculated with or without saturation of the excitation for various values of the nuclear spin.
A density-matrix approach has been developed for the angular distribution and polarization of radiative emission during single-photon atomic transitions for a general set of steady-state excitation processes in an arbitrary arrangement of static (or quasistatic) electric and magnetic fields. Particular attention has been directed at spectroscopic observations in the intense fields of the high-power ion diodes on the Particle Beam Fusion Accelerator II (PBFA II) and SABRE devices at Sandia National Laboratories and at magnetic-field measurements in tokamak plasmas. The field-dependent atomic eigenstates are represented as expansions in a complete basis set of field-free bound and continuum eigenstates. Particular emphasis has been given to directed-electron collisional excitations, which may be produced by an anisotropic incident-electron velocity distribution. We have allowed for the possibility of the coherent excitation of the nearly degenerate field-dependent atomic substates, which can give rise to a complex spectral pattern of overlapping Stark-Zeeman components. Coherent excitations may be produced by a beam of electrons that are spin-polarized at an angle with respect to the propagation direction or by nonparallel electric and magnetic fields. Our main result is a general expression for the matrix elements of the photon-polarization density operator representing the total intensity, angular distribution, and polarization of the atomic radiative emission. For the observation of radiative emission in the direction of the magnetic field, the detection of linearly polarized emission, in addition to the usual circularly polarized radiation, can reveal the presence of a perpendicular electric field or a coherent excitation mechanism.
Racah algebra and standard irreducible tensor techniques show that the probability of two-photon absorption followed by fluorescent decay can be written as a product of two terms with in a series of summations. One term embraces the electric-dipole interactions between the radiation fields and the atomic system and the other, a geometric term, depends upon the choice of experimental orientation and the polarisation of the fields. Examination of the geometric term allows the angular distribution of the radiation emitted following two-photon absorption to be investigated for different atomic coupling schemes for counterpropagating light beams of arbitrary polarisation.
It is shown that the spin and orbital angular momentum of electric dipole photons have the same operator structure and may differ from each other only by spatial dependence in the very vicinity of the atom. It is shown that the photon twins created by a dipole forbidden transition can manifest the maximum entanglement with respect to the angular momentum. It is shown that the states of photons with projection of angular momentum m=0m=0m=0 are less stable than those with m=±1m= \pm 1m=±1.
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.