Control of superradiation bursts arising from a nonlinear optical cavity containing a closely packed chain of atoms

In this paper, we introduce a physically realizable model which contains three externally controllable agents and study how variations of these agents can lead to generation of high-intensity superradiant bursts. To this end, a chain of closely packed quantum emitters (two-level atoms) is placed inside an optical cavity, filled by a second-order nonlinear material. The closeness of the emitters in the chain calls for emitter-emitter interaction, which we explicitly take into account. The model presented here therefore includes three effects: atom-photon coupling, atomic spacing in the chain, and nonlinearity strength, making the model the most realistic among those previously reported. The main aim of the present work is to study the interplay of these three. We pursue this aim by numerically calculating the time evolution of the density operator that describes the whole system, thereby obtaining relevant mean values. To simulate the system, the latest versions of the QuantumOptics.jl and CollectiveSpins.jl packages, within the julia programming language, are employed. For tangible results, the emission rates as a function of time arising from such a system are presented. To verify the correctness of our computational method and for later comparison we also include a reproduction of the previously reported models. From this comparison we conclude that the total Hamiltonian which contains all three controlling parameters can produce much more intense superradiation bursts. Moreover, contour diagrams of the maximum values of the emission rates, in terms of these parameters, are also presented. From such diagrams one can readily read the parametric values for which the superradiation mode is enhanced. A detailed physical discussion of the latter is also presented. It is thus feasible that the results of the present work will help engineer an effective system which exhibits intensive superradiation.