Vacuum Rabi splitting in a coupled system of single quantum dot and photonic crystal cavity: effect of local and propagation Green's functions.

We investigate the light emission characteristics for single two level quantum dot (QD) in a realistic photonic crystal (PC) L3 cavity based upon the local coupling strength between the QD and cavity together with the Green's function in which the propagation function related to the position of the detector is taken into account. We find for a PC cavity that the line shape of the propagation function in frequency domain is identical to that of the cavity and independent on the detector's position. We confirm that this identity is not influenced by the horizontal decay of the cavity. Furthermore, it is revealed that the vacuum fluorescence spectrum of the coupled system never give the triplet in strong coupling regime. Our work demonstrates that the experimental spectral-triplet in coupled system of single QD and PC cavity cannot be individually understood by vacuum Rabi splitting without including other physics mechanism.