We consider ensembles of two level atoms interacting with the field in one mode resonator; such ensembles are homogeneous, if the force of interaction is the same for all atoms. We represent the results of numerical simulation of the following effects: relaxation of atomic excitation for one atom, dephasing assisted transport of energy along the chain of optical cavities (DAT), optical conductivity of a network of cavities, quantum bottleneck, thermal attractors for two atomic systems and ensemble Rabi oscillation for a hundred of atoms and dark states. The last effect required the supercomputer simulation on Lomonosov-2. DAT and quantum bottleneck play the peculiar role in biology (FMO light harvesting complex in green sulfur bacteria), dark states are significant for quantum computations. This elucidates the special role of dark states in such ensembles and the power of finite dimension models of QED, which allow inclusion of dipole-dipole interaction and nonlinearity that makes such models very powerful.
We describe computer methods of simulation of Tavis-Cummings based quantum models, and apply those methods to specific tasks, conductivity measurements of atomic excitations in short chains of optical cavities with two-level atoms, C-Sign optical model, and dark states. For the conductivity measurements, we reproduce the dephasing assisted transport and quantum bottleneck effects and show their relation, and study the "which way?" problem. For the C-Sign optical model, we use the model to find optimal parameters of the system to minimize the error. For dark states, we study their collapse due to dephasing noise.
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