coherence time of $\tau_{\mathrm{corr}}$ = 24 ps was estimated.

For an ideal (homogeneous, disorder-free) condensate a linewidth of $\Delta E \approx 0.66 \,  h / \tau_{\mathrm{coh}} = 0.66 \, h / 8.7~{\mathrm{ps}} = 0.31~{\mathrm{meV}}$ would be expected for the condensate emission according to the Wiener-Khinchin theorem [@Saleh.2008] (and even less assuming the corrected values for $\tau_{\mathrm{coh}}$), where $h$ is the Planck constant. This is about a factor of 6.5 smaller than the observed minimum linewidth of 2 meV for the condensate emission in this experiment. Since the investigated condensate is a complex quantum system including spatial density and phase fluctuations we assume that the Wiener-Khinchin theorem cannot be applied here. We rather suppose that the mechanism which causes a broadening of the emission linewidth (e.g. repulsive particle interaction [@Porras.2003]) does not affect the coherence time to the same extent. This is supported by the quantitative discrepancy between the emission linewidth and the coherence time, which is observed also in a CdTe [@Kasprzak.2006] as well as in a ZnO MC. [@Lai.2012] We note that despite of the fast decay of polaritons, condensate emission can be observed up to 90 ps after the arrival of the exciting laser pulse, which thus allows 