Transport of Photonic Bloch Wave in Arrayed Two-Level Atoms

In a quantum system of arrayed two-level atoms interacting with light, the interacted (dressed) photon is propagating in a periodic medium and its eigenstate ought to be of Bloch type with lattice symmetry. As the energy of photon is around the spacing between the two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Therefore an energy gap exists in the dispersion relation of the photonic Bloch wave of dressed photon in addition to the nonlinear behaviors due to atom-light interactions. There follows several interesting results which are distinct from those obtained through a linear dispersion relation of free photon. For example, slow light can exist, the density of state of dressed photon is non-Lorentzian and is very large around the energy gap; the Rabi oscillations become monotonically decreasing in some cases; and besides the superradiance occurs at long wavelengths, the spontaneous emission is also very strong near the energy gap because of the high density of state.