Fig. 2: Extraction of the g⁽¹⁾ from stationary and circulating states in both a hexagon and heptagon.

a, b Real- and Fourier-space PL imaging of a hexagon and heptagon in different coupling configurations achieved by tuning the polygon radius. Two leftmost columns show condensation of a hexagon into in-phase (m = 0) and anti-phase (m = 3) configurations, whereas four rightmost columns show in-phase (m = 0) and vortex formation (m = ± 1, ±2, ±3) of a heptagon. c Extracted (red crosses) and calculated (black dots) mutual first-order coherence g⁽¹⁾ versus parameter d extracted from the interferogram between condensates for different polygon configurations. The values of g⁽¹⁾ lie upon the continuous function (green dot-dashed line) given by \({g}^{(1)}(x)=\cos (2\pi mx/N)\), where x has replaced the discrete parameter d. The point at d = 0 corresponds to the autocorrelation of the condensate wavefunction at zero time delay and is set as g⁽¹⁾(0) = 1. The radii of the polygons are written in the top left hand corner of the real-space images in a. All real- and Fourier-space images are plotted on the same scale defined on the scale bar at the end of each row.