Topological speckles

The time evolution of a topological Su-Schrieffer-Heeger chain is analyzed through the statistics of speckle patterns. The emergence of topological edge states dramatically affects the dynamical fluctuations of the wavefunction. The intensity statistics is found to be described by a family of noncentral chi-squared distributions, with the noncentrality parameter reflecting on the degree of edge-state localization. The response of the speckle contrast with respect to the dimerization of the chain is explored in detail as well as the role of chiral symmetry-breaking disorder, number of edge states, their energy gap, and the locations between which the transport occurs. In addition to providing a venue for speckle customization, our results appeal to the use of speckle patterns for characterization of nontrivial topological properties.