Fig. 4
From: First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas
Emergence of coherence for a Bose–Einstein condensed photon gas. a Maps of the fringe visibility with transverse position for increasing ratios N/N c = {1.01; 1.04; 1.14; 1.26; 1.47; 1.76} showing a strong increase in the coherence, which indicates the onset of long-range order. The size of each image corresponds to 40 µm × 40 µm. b Corresponding variation of the fringe visibility (radially averaged) with distance from the center for different total photon numbers. The measured data (symbols) is accompanied by numerical simulations (solid lines) after taking into account the noise characteristics of the used EMCCD detector and the uncertainty in the experimental determination of the total photon number (shaded areas). c Measured transverse coherence length, with the dots (square) corresponding to data recorded with pulsed (cw) pumping, respectively, vs. N/N c (bottom axis) and phase-space density \(\tilde n\) λ th 2 (top axis) along with theory for the coherence length with (dashed line) and without (solid) numerically implementing technical limitations. Far below the threshold to a Bose–Einstein condensate, the transverse coherence length equals \({\lambda _{{\rm{th}}}}\sqrt {\ln 2/4\pi } \) (dashed-dotted line), and upon reaching Bose–Einstein condensation the ensemble becomes transversally coherent, with correlation lengths exceeding the 12.7 µm FWHM of the condensate mode (blue solid line). The error bars represent the uncertainty (s.d.) in the determination of N/N c
