Supplementary Figure 1 Schematic layer layout of the two dimensional optical cavity. The vertical optical confinement is realized by epitaxially grown distributed Bragg reflectors. The active part consists of single wavelength thick GaAs cavity layer with InGaAs quantum dots in the centre acting as atomic-like emitters. In order to obtain three dimensional optical confinement the layer structure is patterned by lithography and etching to create cylindrical pillars with various lateral dimensions. Supplementary Figure 2 Temperature dependence of PL spectra for a 1.5 m microcavity (Q = 7300) showing the tuning of a single QD exciton through resonance with the cavity mode in the weak coupling regime. In contrast to the strong coupling case (see Fig. 4) a crossing of the quantum dot exciton (X) and microcavity photon mode (C) is observed.