Direct and mediated dipole-dipole interactions in a reconfigurable array of optical traps

Optically levitated nanoparticles in vacuum experience both electrostatic and light-induced dipole-dipole interactions, offering a versatile platform to explore mesoscopic entanglement and many-body dynamics. A significant challenge in optical trap arrays is to achieve site-resolved, point-to-point tunability: adjusting the laser parameters of a single trap typically induces global cross-talk to neighboring sites, hindering independent control. Inspired by tunable couplers in superconducting circuits, we implement an ancillary nanoparticle that functions as a coupler between two target nanoparticles. Within a reconfigurable three-particle array, we demonstrate broad tunability of the direct dipole-dipole interaction by controlling the phase and position of the traps. In addition, we observe spectral signatures consistent with mediated interactions between the target particles via the ancillary one, manifested as mode participation beyond the uncoupled response. Our results establish a practical route to tailored, site-resolved control in multi-particle optical trap arrays, expanding the optical-binding toolbox and opening opportunities for programmable oscillator networks relevant to macroscopic quantum mechanics and precision sensing.