Fig. 4: Single shot of a pentagon of polariton condensates with a doubly charged vortex at the centre.

Pentagon condensate with a charge m = 2 vortex. a Experimental real-space PL and b, c phase extracted from interferometry from a single instance of the condensate. Simulated steady state m = 2 vortex wavefunction d real-space density, g Fourier-space density, and e, f real-space phase. c, f Zoomed-in regions of the dashed squares in b, e, respectively. h Phase difference between adjacent condensates (black dots) around the polygon extracted from the black circles in b. The red line is the expected phase difference of θi,i+1 = 4π/5. Green and blue dash-dotted lines mark the maximum deviation. i Line profile extracted along the black circle in c, f demonstrating a full 4π phase winding. Yellow dots correspond to azimuthal angle equal to zero. Experimental data are represented by the coloured disks and numerical simulation by the black-dotted curve.