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Journal of Physics B Atomic and Molecular Physics

Scattering of light by an electron in the presence of a magnetic field and a strong microwave field

Sándor Varró, F. Ehlotzky, János A. Bergou

Published Feb 14, 1984• 10 citations
Publisher

Abstract

Scattering of light by an electron embedded simultaneously in a uniform magnetic field and in a microwave field is first analysed within the framework of classical electrodynamics. It is shown that the intensities of the different components of the scattered light can be increased by the presence of the magnetic field. Then coherent quantum states of the electron in the same field configuration are constructed and are applied to the description of the scattering process using semiclassical methods. The results of the classical and semiclassical calculations are compared and discussed and various limiting cases are considered to show the connection with previously published work.

DOI
10.1088/0022-3700/17/3/017

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Scattering of light by an electron embedded simultaneously in a uniform magnetic field and in a microwave field is first analysed within the framework of classical electrodynamics. It is shown that the intensities of the different components of the scattered light can be increased by the presence of the magnetic field. Then coherent quantum states of the electron in the same field configuration are constructed and are applied to the description of the scattering process using semiclassical methods. The results of the classical and semiclassical calculations are compared and discussed and various limiting cases are considered to show the connection with previously published work.
By continuing earlier investigations, generalized coherent states are introduced to describe the quasiclassical motion of electrons in a microwave and in a homogeneous magnetic field. The microwave is circularly polarized and propagates along the direction of the magnetic field. In view of possible applications to laboratory plasmas, the problem is treated nonrelativistically and the microwave is taken in the dipole approximation. The generalized coherent states emerge in polar coordinates (\ensuremath{\rho},\ensuremath{\varphi}) from ordinary Landau states \ensuremath{\Vert}l,m> by an appropriate choice of unitary and displacement operations. These coherent states are shown to form a complete and orthonormal set. Consequently, these states may be conveniently used for the description of scattering processes. As an example, scattering of electrons by a screened Coulomb potential is considered in the presence of the above two external fields. For simplicity, the scattering potential is treated in the first-order Born approximation. The quasiclassical features of the corresponding cross sections for the induced nonlinear processes are discussed.
In the present work we construct coherent states in the magnetic–solenoid field, which is a superposition of the Aharonov–Bohm field and a collinear uniform magnetic field. In the problem under consideration there are two kinds of coherent states, those which correspond to classical trajectories which embrace the solenoid and those which do not. The constructed coherent states reproduce exactly classical trajectories, maintain their form under the time evolution and form a complete set of functions, which can be useful in semiclassical calculations. In the absence of the solenoid field these states are reduced to the well known in the case of uniform magnetic field Malkin–Man'ko coherent states.
Quantum-electrodynamic processes that take place in the presence of a squeezed electromagnetic field are discussed. Integral formulas are derived that make it possible to express the probability of any process in a squeezed electromagnetic field in terms of the probability of the same process in a classical electromagnetic field. The main laws that govern processes of first order in the fine-structure constant as functions of the number of photons involved and the quantum fluctuations are examined. Tunneling formulas for the probability of a photon producing an electron-positron pair in a strong squeezed field are derived. Also, resonant electron-electron scattering is examined and the scattering cross section as a function of the statistical properties of the field (the way the field has been squeezed) is investigated. It is found that the quantum fluctuations of the squeezed electromagnetic field give rise to an increase in the scattering cross section, with the probability of the process in a phase-squeezed electromagnetic field always being higher than the probability of the process in an amplitude-squeezed electromagnetic field.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
The classical or semiclassical theory presented in Chapter 2 gives a satisfactory account of light-matter interactions in some cases. However, a detailed understanding of different processes requires a quantum mechanical theory of radiation. The quantum theory of light, like classical theory, is also based on Maxwell's equations. However, in quantum theory the electric field F and the magnetic field H are treated as operators. This chapter develops the correspondence between the two and outlines the method for converting field vectors F and H into quantum mechanical operators. Topics discussed include wave equation in a rectangular cavity, quantization of the electric field, time-dependent perturbation theory, interaction of an electron with the magnetic field, and second-order perturbation theory. Exercises are provided at the end of the chapter.