Quantum theory of exciton polaritons in cylindrical semiconductor microcavities

A quantum-mechanical formalism is developed in order to study the interacti on between a quantum-well exciton and the electromagnetic (e.m.) field insi de a cylindrical microcavity. The cavity modes are evaluated as a function of the radius according to a self-consistent procedure, and are found to be in good agreement with the experiment [J.M. Gerard, D. Barrier, J. Y. Mart in, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, A ppl. Phys. Lett. 69, 449 (1996)]. The cavity polaritons are then evaluated by diagonalizing the total Hamiltonian, which is written in second quantize d form and includes also the self-interaction term. The mixed radiation-mat ter states manifest themselves with the characteristic anticrossing behavio r. The Rabi splitting is found to depend on the quantum numbers of the mode and on its polarization: for a large radius of the cavity it approaches th e planar cavity limit, and it decreases for decreasing radius. This effect is interpreted in terms of the leakage of the cavity modes in the outside r egion, which decreases the overlap between the exciton wave function and th e e.m. field. Although the interaction between material and radiation excit ations with the same quantum numbers still remains the dominant one, differ ent boundary conditions applying to the exciton and to cavity mode wave fun ctions lead to interactions between states with different radial quantum nu mbers. Removal of the exciton degeneracy is predicted: the large energy sep aration between radiation modes with different quantum numbers produces an energy splitting of the otherwise degenerate exciton states inside a cylind rical microcavity. [S0163-1829(99)11847-2].