@article { , title = {Engineering NonBinary Rydberg Interactions via Phonons in an Optical Lattice}, abstract = {Coupling electronic and vibrational degrees of freedom of Rydberg atoms held in optical tweezer arrays offers a flexible mechanism for creating and controlling atom-atom interactions. We find that the state-dependent coupling between Rydberg atoms and local oscillator modes gives rise to two- and three-body interactions which are controllable through the strength of the local confinement. This approach even permits the cancellation of two-body terms such that three-body interactions become dominant. We analyze the structure of these interactions on two-dimensional bipartite lattice geometries and explore the impact of three-body interactions on system ground state on a square lattice. Focusing specifically on a system of Rb87 atoms, we show that the effects of the multibody interactions can be maximized via a tailored dressed potential within a trapping frequency range of the order of a few hundred kilohertz and for temperatures corresponding to a >90\% occupation of the atomic vibrational ground state. These parameters, as well as the multibody induced timescales, are compatible with state-of-the-art arrays of optical tweezers. Our work shows a highly versatile handle for engineering multibody interactions of quantum many-body systems in most recent manifestations on Rydberg lattice quantum simulators.}, doi = {10.1103/physrevlett.124.043402}, eissn = {1079-7114}, issn = {0031-9007}, issue = {4}, journal = {Physical Review Letters}, publicationstatus = {Published}, publisher = {American Physical Society}, url = {https://nottingham-repository.worktribe.com/output/3842446}, volume = {124}, keyword = {General Physics and Astronomy}, year = {2020}, author = {Gambetta, F.?M. and Li, W. and Schmidt-Kaler, F. and Lesanovsky, I.} }