Engineering NonBinary Rydberg Interactions via Phonons in an Optical Lattice
Filippo Maria Gambetta, Weibin Li, F. Schmidt–Kaler, Igor Lesanovsky
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 ^{87}Rb 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.