Seeing quantum correlations through an excitonic lens

Two-dimensional materials provide a fascinating playground for exotic and strongly correlated phenomena of quantum particles. However, current optical experiments that aim to explore the microscopic organization in these materials face an important challenge arising from the optical diffraction limit. The mismatch between the dispersion relation of light and that of the collective many-body excitations of the two-dimensional material constrains the optical measurements to probe matter correlations that fall inside a narrow region in momentum space, the so-called light-cone. Here, we present a protocol for circumventing these constraints through an excitonic lens, which (i) probes with the high-momentum matter correlations of the two-dimensional material through Coulomb interactions, and (ii) implements a Fourier transformation that converts the probe excitonic fields that lie outside of the light-cone to low-momentum fields inside the light-cone. Moreover, the excitonic lens allows correlation functions in momentum space to be read off from the spatial correlations of the output light. We evaluate the performance of our method by numerically simulating an experiment where the signatures of a subwavelength pattern formation can be measured.