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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

On the interaction of harmonic oscillators with the radiation field

Kazimierz Rza̧żewski, W. Żakowicz

Published Feb 1, 1971• 4 citations
Publisher
DOI
10.1007/bf02815271

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It is pointed out that induced radiation effects cannot be purely quantum in nature and that they must be present in the classical theory of radiation processes. The classical theory is usually built on the example of the harmonic oscillator. Several effects arising from the interaction of the oscillators with the field disappear when harmonic oscillators are considered. This is particularly true when one is concerned with radiation processes induced by the field. In addition, the interaction between the field and the radiation of nonlinear oscillators (their frequencies depend on the energy) was not previously considered from the standpoint of the classical theory. Because of these reasons and because of the interest in the problem of quantum generators the question of the role of induced radiation in classicai theory was examined. The theory is described, and some specific properties of the classical system are contrasted with those of the quantum system. The description includes a discussion of spontaneous radiation processes and both harmonic and anharmonic oscillators are considered. The limiting transition from quantum to classical theory is discussed, and a detailed comparison of the two more » theories is made. An ensemble of oscillators distributed in energy is discussed in the classical theory. It is shown, for certaln determined conditions, that classical systems do not absorb but rather enhance incident radiation. (TTT) « less
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
By applying a Lie-algebra method [Phys. Rev. A 42, 4302 (1990); 47, 5213(E) (1993)], we obtain analytical solutions and energy eigenvalues for a charged harmonic oscillator interacting with a single-mode photon field. The energy shifts of bound states of the harmonic oscillator due to the radiation field is also derived. By a variational method, we show that any bound state in a central potential which satisfies a power law can be treated as a harmonic oscillator around its average radial position. With this idea, we generalize the energy-shift formula obtained for a harmonic oscillator to the hydrogen-atom case. Our result shows that the energy shifts depend on the principal quantum number according to an inverse-square law.