The strong coupling regime between excitons in a single self-assembled InAs quantum dot and the cavity mode in a photonic-crystal structure embedded in GaAs planar waveguides is theoretically investigated. It is concluded that zero-dimensional mixed states should form when the quality factor of the cavity mode is higher than Q ~2000. The corresponding vacuum-field Rabi splitting is close to its limiting value already for Q~10000. Results are shown for a model GaAs-based photonic crystal nanocavity, in which single quantum dot excitons are predicted to be always in the strong coupling regime if the quantum dot is placed close to the antinode position of the electric field.
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