Low-dimensional systems in condensed matter physics exhibit a rich array of correlated electronic phases. One-dimensional systems stand out in this regard. Electrons cannot avoid each other in 1D, enhancing the effects of interactions. The resulting correlations leave distinct spatial imprints on the electronic density that can be imaged with scanning probes. Disorder, however, can destroy these delicate interacting states by breaking up the electron liquid into localized pieces. Thus, to generate fragile interacting quantum states, one requires an extremely clean system in which disorder does not overcome interactions, as well as a high degree of tunability to design potential landscapes. Furthermore, to directly measure the resulting spatial correlations, one requires an exceptionally sensitive scanning probe, but the most sensitive probes presently available are also invasive, perturbing the system and screening electron-electron interactions. / Engineering and Applied Sciences