Level-degeneracy effects in super-radiance theory. Calculations forj=12toj′=12dipole transition

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Abstract
We study here level-degeneracy effects in super-radiance, using the quantum "small-system" model whose interest and limitations are discussed. First, we show that this model allows one to understand the physical origin of these effects and to describe their qualitative influence on the properties of the emitted light. We also present and analyze numerical results obtained for the case of a dipole transition between two degenerate levels of angular momenta ½. We show that in this particular case one can define a basis of collective states which is well adapted to the invariance properties of the master equation. It is then possible to solve the master equation and to compute expectation values for the radiated field (intensity radiated with a given polarization, quantum fluctuations of this intensity) for various initial conditions and for small but already significant values of the number of individual systems. A detailed analysis of these results and a comparison with analogous calculations in the case where the degeneracy is supposed to be removed allows us to estimate the individual influence of the different types of effects (interference effects and the two sorts of competition effects, inhibition and initiation). We also compare the total intensity radiated to the intensity radiated by the same number of two (nondegenerate) level atoms. This comparison can be simply understood if one studies the partition of the population of the collective energy levels between the different states of these levels, and it appears that the most populated states are these which are able to radiate the most. Finally, it is shown how level degeneracy affects the quantum fluctuations of the intensity.