Application of Green's Functions to Radiative Cooperative Effects in Multiatom Systems

Spontaneous-radiation processes associated with a number of multiatom systems are studied. Green's-function techniques are used in conjunction with a model of $N$ two-level atoms interacting with a quantized radiation field to investigate the assumption of the independence of the spontaneous-radiation properties of a given atom from the states of the other atoms in the system. It is shown that the natural linewidth of an excited atom in the presence of a deexcited atom is different from that of an isolated excited atom. For interatomic separations smaller than a critical separation, the two-atom system is best considered as a collective unit with regard to its spontaneous-radiation properties. The influence of these "radiative cooperative effects" is studied also for the systems of two initially excited atoms. Also the influence of radiative cooperative effects in the scattering of a photon by a system of two deexcited atoms is studied. It is shown that the frequency distribution of the scattered radiation exhibits a double-peak structure for interatomic separations smaller than $\frac{3}{4}\lambda$. The techniques of Green's functions are then applied to the study of radiative cooperative effects in several many-atom systems. It is shown that within the context of the model certain information is obtained exactly via the Green's-function techniques as applied to the manyatom problems of a single excited atom in the presence of $N\gg 1$ deexcited atoms and the scattering of a photon by a system of $N\gg 1$ deexcited atoms. The necessity of treating manyatom systems from a "collective" point of view is easily seen from our results.