Polariton band structure in III-V semiconductors doped with an ordered chain of identical two-level quantum dots or quantum wells

In this paper, we study quantum electrodynamics of III-V semiconductors doped with an ordered chain of identical two-level atoms. To find the dispersion relation of the polariton-atom system, we diagonalize the Hamiltonian in the one-polariton sector of the entire Hilbert space. We found that when the atomic resonance frequencies of two atoms lie inside the polariton gap, the spectrum of the system contains polariton-atom bound states. For finite interatomic distances these states form energy band due to an effective atom-atom interaction. The above phenomenon can be observed in III-V semiconductors doped with an array quantum dots or quantum wells where a quantum well or a quantum dot will act as a two-level system. Numerical calculations for impurity band and effective mass are performed for AlAs.