Collective Decay Modes of Many Nonoverlapping Two-Level Atoms — An Outline
We treat quantum mechanically the emission of N≥1 photons into the continuum of modes, the photons being radiated by J≥N nonoverlapping, not necessarily identical, two-level atoms at given positions. Initially, at t = 0, there are no photons, but any N atoms are excited. Only one ad hoc assumption and two well justified standard approximations are needed to get in five essential steps a “closed” solution of this rather complex problem: (i) We start with “exact” equations of motion in the sense of a certain variant of QED. (ii) We assume ad hoc that the atoms are “two-level” atoms. This puts the theory into the framework of Hilbertspace quantum mechanics. (iii) A variant of the rotating wave approximation allows essential simplifications. Its proven applicability shows that semiclassical approaches to many-photon collective phenomena cannot be justified quantum mechanically. (iv) All desired solutions of the simplified equations allow an exact separation of the dependence on photon momentum angles and spins from the dependence on time and frequencies. The latter is controlled by given “radial” equations. (v) These equations can be solved analytically if the distances between the atoms permit within the natural lifetime of a single atom the exchange of many “causal photon signals” between any two atoms.
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