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Physical Review

Cooperative Phenomena in Quantum Theory of Radiation

A. Gamba

Published May 1, 1958• 10 citations
Publisher

Abstract

Cooperative phenomena in a radiating system have been discussed by Dicke. A new formulation of the theory is presented, which shows more clearly the relations of these effects with the quantum-mechanical identity principle. Some theoretical and practical implications of the theory are pointed out.
DOI
10.1103/physrev.110.601

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Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•May 2, 1932•99 citations
Phenomena of coherent resonant propagation can be considered as resulting from the cooperative interaction of a certain number of excited two-level systems. It is shown that these phenomena can be characterized by a specific "maximum cooperation number" and by the associated "cooperation time." These are defined for the superradiant state, but their meaning and usefulness can be extended to other situations. The alternative description of of superradiance as a spontaneous or as a stimulated effect is also discussed and it is shown that with the help of the new concepts, the Dicke quantum perturbative treatment can be reconciled with the semiclassical theories.
The Dicke theory of coherent spontaneous emission is generalized by means of group-theoretical methods. Effects of superradiation and the structure of coherent responses of an equilibrium medium to pulsed excitation are considered. A method of calculating cooperative effects in second-order perturbation theory is developed. The role of collective properties of a system of radiators in experiments with high power exciting radiation is discussed. Some "anomalous" features of stimulated Raman scattering are accounted for.
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance.
Biophoton emission (PE) method is a non-invasive way revealing biophysical interactions in living tissues. Since its mechanism is not very clear, its acceptance is limited. Gu has presented the quantum theory on biophoton emission according to the Dicke model. However, the Dicke model does not apply to biological system. In this paper, we studied PE by using the identical particle model, the interaction of identical particles by quantum chemistry, as well as the transition of the system interacting with radiation by the time quantum theory on radiation-matter interaction put forward by the first author and his cooperators. It was shown that the identical particles form coherent states, the photon emission probability of the superradiant state is a liner function of N and N2, and the one of the subradiant state is zero. In other words, the photon emission intensity represents the coherent states of the identical particle system. The linear relationship of N and N2 agrees with the PE experiment results on early drosophila embryos. The research on the cell division cycle showed that the superradiant states correspond to the late S phase. This is why PE can be used to differentiate human tumor tissues from normal ones. We also studied induced PE.
Abstract It will probably be agreed that among all the recent developments of the quantum theory, one of the least satisfactory is the theory of radiation. The present paper is intended as a preliminary to a new line of attack on the subject. It was begun some time ago, but owing to lack of success in carrying it to a conclusion, its publication has been much delayed. In the meantime other papers have appeared, which in some respects follow the same train of thought. The authors of these works have carried their methods further in some directions than I have attempted, but there is still perhaps room for the discussion of a number of questions from the rather different point of view adopted here. 1. The main principle of the present work is the idea that, since matter and light both possess the dual characters of particle and wave, a similar mathematical treatment ought to be applied to both, and that this has not yet bee done as fully as should be possible. Whereas we have a fairly complete calculus for dealing with the behaviour of any number of electrons or atoms, for photons the existing processes are much less satisfactory. The central difficulty, which makes it hard to apply the ordinary methods of wave mechanics to light, is the fact that (at least according to our present ideas) photons can be created and annihilated, and to represent this in a wave system we have to be able to think of a medium suddenly coming into existence and then going out again, when the light that it was carrying is absorbed. Such behaviour is a grave difficulty in the way of allowing us to think of the photon as a wave, and tends to make us think with more favour of its particle aspect, until we recall that after all it is quite unlike any known particle to come into existence and later to disappear without trace. The theories at present current, such as that of Heisenberg and Pauli, avoid these difficulties because they are mainly formal generalisations of the classical theory; this frees them from the above difficulties, but they pay for it in being highly abstract, and, as it has turned out, rather unsuccessful.