This report quantum mechanically analyses a system composed of a two-level system, a single mode cavity, and free space photon modes, which are coupled to each other. The analytical solution in the intermediate regime between the strong and weak coupling regimes is successfully obtained. It is found that the emission rate reaches its maximum when the cavity photon lifetime τcav satisfy 1/τcav = 4|g|, where 2|g| is the vacuum Rabi frequency. Also, Fano resonance is shown to occur under certain conditions. These results can be useful for high-speed single photon sources and for fundamental understanding of the interaction between a quantum dot and a cavity mode. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.