The response of an electron system to electromagnetic fields with sharp spatial variations is strongly dependent on quantum electronic properties, even in ambient conditions, but difficult to access experimentally. We use propagating graphene plasmons, together with an engineered dielectric-metallic environment, to probe the graphene electron liquid and unveil its detailed electronic response at short wavelengths. The near-field imaging experiments reveal a parameter-free match with the full theoretical quantum description of the massless Dirac electron gas, in which we identify three types of quantum effects as keys to understanding the experimental response of graphene to short-ranged terahertz electric fields. The first type is of single-particle nature and is related to shape deformations of the Fermi surface during a plasmon oscillation. The second and third types are a many-body effect controlled by the inertia and compressibility of the interacting electron liquid in graphene. We demonstrate how, in principle, our experimental approach can determine the full spatiotemporal response of an electron system.The quantum physics of electron systems involves complex short-distance interactions and motions that depend sensitively on electron correlations and Fermi surface deformations.1,2 These are often considered irrelevant in optical and transport measurements, which probe the response to electrical fields with long length scales. When free electron systems are driven by electric fields varying rapidly in both time and space, however, the response pattern in dynamical current reveals these complex shortrange effects. This aspect of electron response, known as non-locality or spatial dispersion in conductivity, arises due to the internal spreading of energy via the moving electrons. Even in ambient conditions (as Fermi liquid parameters depend on temperature weakly 1,2 ), the spatial dispersion in an electron system retains a detailed connection to Fermi-surface and electron-electron correlation effects, and hence it provides a unique window into quantum theories of electron systems without requiring extremes of low temperature or high magnetic field. Unfortunately, these quantum regimes cannot be accessed by standard optical and transport probes.Plasmons-electric waves resulting from an inertial electron conductivity combined with electric restoring * Marco.Polini@iit.it † frank.koppens@icfo.eu forces-can act as a carrier of the spatiotemporal electric fields necessary to probe non-locality. All systems exhibit non-local effects for plasmon wavelengths approaching the electronic Fermi wavelength λ F , which has been confirmed in experimental studies of metals and semiconductor two-dimensional (2D) electron gases. 3-5 Such experiments have however led to challenges in quantitative interpretation, due to strong interactions that go beyond standard (e.g. random phase approximation) theoretical treatments, 3,4 and possible complications by edge effects and tunneling.
5-9In graphene, it is possible to access a diff...