Fig. 2: Observation of exponential channel density profiles.

a–c The top images in each column show the mask applied to the spatial light modulator (white indicates bright pixels). The second row of images shows the density obtained from Gross–Pitaevskii simulations after 250 ms. The third row of images show an average of three experimental absorption images after 250 ms of evolution, each with different disorder realisations. The channel density profiles show semi-logarithmic snapshots of the channel density (in units of atoms per 2.1 μm camera pixel length), at times (50, 100, 150, 200, and 250) ms of time evolution, with the density integrated across the y-direction. Each increasing-time snapshot is offset for clarity by a factor of 10. Profiles are overlaid with an exponential fit to the data in blue, and with the density profiles from the GPE simulation in red. Details of the geometry are: a η = 0.07, (r, L, w) = (43, 180, 36) μm; b η = 0.17, (r, L, w) = (43, 108, 58) μm; c η = 0.32, (r, L, w) = (43, 108, 58) μm. d The apparent localisation length is found at each time evolution from the weighted exponential fit to the channel profile for two values of η, with (r, L, w) = (43, 108, 58) μm. Results from GPE simulations are shown as solid lines. e The localisation length is found as an average of apparent localisation lengths for times 210–250 ms, for two channel geometries. Numerical simulation data is also plotted (joined circles). Errorbars show standard deviations obtained from three trials with different disorder realisations. Dotted lines indicate the channel lengths of 180 and 108 μm of the two different geometries. Note that the experimental data for w = 58 μm is shown for η = 0.17 and η = 0.32 only.