Artificial atoms, such as quantum corrals, offer an excellent platform to study fundamental interactions between localized quantum states and nanoscale probes. We performed atomic force microscopy measurements inside square quantum corrals on Cu(111) using CO- and metal-terminated tips. Using chemically unreactive CO-terminated tips, repulsive Pauli forces can be probed, while metallic tips are attracted to the localized quantum states due to chemical bonding. We found distinct exponential decay constants of (46±6) pm for the repulsive and (66±5) pm for the attractive forces. Attractive and repulsive interactions between two natural atoms show significantly shorter decay lengths. While natural atoms feature states with a broad range of decay lengths, including very short ones from deeply bound states, quantum corrals are lacking such deeply bound and highly localized states, resulting in longer decay lengths. These results offer an alternate route to understanding and designing atomic-scale interactions in low-dimensional quantum structures and devices.