high condensate densities. We note that the constant sharp stripes in the $I_P(k)$ profile at a specified *k* for all excitation powers are caused by imperfections of the setup, probably due to the microscope objective.

A similar finding with increasing excitation power was also observed for other detunings $\Delta = -50~{\mathrm{meV}},\ldots,-10~{\mathrm{meV}}$, and we conclude that our observation does not depend significantly on the particular choice of detuning within the mentioned range.

To investigate the temporal coherence properties of the condensate we used a Michelson interferometer in the plane mirror (PM) - retroreflector (RR) configuration to superimpose the PL emission of polaritons with opposite emission angles or rather wavevectors. For this experiment, the sample was excited by a frequency-tripled Ti:sapphire laser at 266 nm with a pulse duration of about 2 ps. Further details of the setup are provided in Appendix \[sec:sample\_setup\].

![(color online) (a)-(b): Energy-resolved far-field PL interference pattern in a linear false color scale for $T = 10~K$ and $\Delta = -47$ meV: (a) large path difference $\Delta s$: uncorrelated far-field PL emission (basically the sum of the emission from the individual interferometer arms), (b) path difference close to zero: distinct interference fringes indicating mutual temporal coherence of the 