Resonant scattering of am intense beam of radiation by an arbitrary number of atoms contained in a volume whose dimensions are small as compared to the radiation wavelength is studied. It is seen that the scattered radiation is an equally spaced triplet whose middle frequency is equal to the incident frequency. Counting rates exact to all orders in incident intensity are obtained. Special cases of (i) atoms in ground state, (ii) atoms in excited state, (iii) assembly of atoms in super-radiant state, and (iv) assembly of atoms in thermal equlibrium are studied.
Interaction with a multimode quantized radiation field of an assembly of
N two-level atoms contained in a small volume is considered for the special cases of (i) highly excited, (ii) weakly excited, and (iii) superradiant atomic assemblies, and solutions of equations of motion are obtained in closed form. For (i) and (ii) we show that, if the atomic assembly is in the Dicke state
∣r,m>, the spontaneously emitted radiation is Lorentzian, and its spectral width and the numerical value of the Lamb shift are
r+∣m∣ times that for a single excited atom. For (i) the sign of Lamb shift is opposite to that for (ii) and for a single excited atom. Change in the frequency shift gives chirping in the pulse radiation emitted spontaneously by an assembly of atoms. We obtain the reduced density operator for a single mode and for the complete spontaneous emitted radiation, and discuss its characteristic function, weight function in diagonal representation, coherence functions, and normalized variance. We find that the emitted radiation is chaotic if all atoms are excited or if the assembly is weakly excited and is in thermal equilibrium. For a superradiant assembly, the radiation is coherent; it is only amplitude coherent if the initial atomic density operator is nondiagonal. We also study stimulated emission and scattering for the cases (i) and (ii). For case (iii) these phenomena do not take place.