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Journal of Physics B Atomic Molecular and Optical Physics

Spontaneous radiation by a three-level atom in a dissipative medium

Hui W. Cao, Chang-qi Cao

Published Mar 28, 1995• 5 citations
Publisher

Abstract

Spontaneous radiation by three-level atoms in a dissipative medium (such as plasma) has been investigated by Langevin equations and the modified Weisskopf-Wigner approximation. General formulae for calculating spontaneous emission coefficients, i.e. Einstein A coefficients, are presented. Numerical calculation shows that the dissipation of plasmas can modify the spontaneous emission coefficients significantly and causes a pit in the coefficient-density curves for relatively low temperature plasmas, and also a pit in the coefficient-temperature curves.

DOI
10.1088/0953-4075/28/6/013

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Spontaneous radiation by three-level atoms in a dissipative medium (such as plasma) has been investigated by Langevin equations and the modified Weisskopf-Wigner approximation. General formulae for calculating spontaneous emission coefficients, i.e. Einstein A coefficients, are presented. Numerical calculation shows that the dissipation of plasmas can modify the spontaneous emission coefficients significantly and causes a pit in the coefficient-density curves for relatively low temperature plasmas, and also a pit in the coefficient-temperature curves.
The effect of dissipation of plasmas on the spontaneous radiation of an ionized atom is investigated by Langevin equations and the modified Weisskopf-Wigner approximation to consider the quenching effect of the Einstein A coefficient. The dissipation of field in plasmas results from inverse bremsstrahlung of free electrons and absorption of the ions of the same kind as the radiator. Under certain conditions the Einstein A coefficient may be reduced significantly. The lifetime of the excited ion will be changed correspondingly.
New interesting effects arise, when three-level atoms interact with the plasma, laser field, or a heat bath. If the atoms inside the plasma are excited by the polarized laser pulse or an electron beam, the line wings of the radiation are completely polarized, while the line core is only partially polarized. The Einstein coefficients are generalized to the case, when the atomic decay channels are subject to quantum interference. Such atoms may develop nonzero quantum coherence between upper levels, if they are in contact with the heat bath in thermal equilibrium. This coherency changes the emissivity of the medium and hence can be experimentally observed. In the case when three-level atoms interact with the laser field, spontaneous emission can be suppressed over the whole frequency spectrum.
An explicit calculation of conservation of probability and energy in a two-atom system is presented. One of the atoms is excited initially and undergoes spontaneous emission. The field radiated by this atom can be scattered by the second atom. It is seen that the Weisskopf-Wigner approximation must be applied using a specific prescription to guarantee conservation of probability and energy. Moreover, for consistency, it is necessary to take into account the rescattering by the source atom of radiation scattered by the second atom.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.