An energy-resolved atomic scanning probe
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. Moreover, scanning probes measure the density of states locally at the position of the probe tip, but typically 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 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 can be siphoned from the system of interest by a narrow energy band of non-interacting states. We demonstrate that ultra-cold atomic lattices are a natural platform for implementing this concept and visualize the energy and spatial dependence of the atom density in inhomogeneous, interacting lattices.