Daniel S. Gruss, Chih-Chun Chien, Julio T. Barreiro, Massimiliano Di Ventra, Michael P. Zwolak
The density of states is a concept that is ubiquitous in classical and quantum physics, since it quantifies the energy distribution of states available in a system. Spectroscopic means allow its measurement over the entirety of a system's energy spectrum, but do not generally provide spatial resolution. On the other hand, scanning probes measure the density of states locally at the position of the probe tip, but do not have access to the whole spectrum. Here, we show how the local density of states over the whole energy spectrum can be measured in atomic gases. This energy-resolved atomic scanning probe provides a simple, yet quantitative operational definition of a local density of states for both interacting and non-interacting systems as the rate at which particles (or holes) can be siphoned from the system of interest, S, by a narrow energy band of non-interacting states, the probe P. This links the particle current directly with the density of states, as scanning tunneling microscopy does with the differential conductance, but without suffering from interpretational issues outside of linear response. We demonstrate that ultra-cold atomic lattices - which are increasingly employed in the simulation of many-body phenomena [1-5] - are a natural platform for implementing this concept. Using this approach, we elucidate puzzling features in interaction-induced transport and visualize the energy and spatial dependence of the atom density in inhomogeneous, interacting lattices.