Fig. 5: Numerical and analytical calculations of the spectrum and PL.

a Density profile of the condensate under the conditions of Fig. 1 with the pump placed on the left side of the measured region (solid red line in the horizontal profile). The main plot is on a linear scale and the inset a logarithmic one, showing the asymmetric polariton density of the condensate. b Phase (in radians) of the condensate in 2D space. The region under measurement is shown by the semitransparent rectangle. c, d, Excitation spectrum obtained numerically from the FT of \({g}^{(1)}(\Delta {\bf{r}},\Delta t)\), i.e. following the same procedure as in the experiments, and of \({\left|\psi ({\bf{r}},t)\right|}^{2}\), respectively. In the latter case the ghost branch is weakly populated, but still visible. e, PL from analytical calculations in the Bogoliubov approximation under uniform pumping with finite condensate velocity. Note that in this case both branches are populated.