# Engineering non-binary Rydberg interactions via phonons in an optical lattice

## TL;DR

This paper demonstrates how phonon-mediated, controllable multi-body interactions in Rydberg atoms within optical lattices can be engineered, enabling advanced quantum simulation capabilities with current experimental setups.

## Contribution

It introduces a method to control and cancel two-body interactions, emphasizing the creation of dominant three-body interactions in Rydberg atom systems.

## Key findings

- Controllable two- and three-body interactions via phonon coupling.
- Cancellation of two-body interactions to favor three-body effects.
- Feasible implementation within existing optical tweezer arrays.

## 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 multi-body interactions can be maximized via a tailored dressed potential within a trapping frequency range of the order of a few hundred kHz and for temperatures corresponding to a $ >90\% $ occupation of the atomic vibrational ground state. These parameters, as well as the multi-body induced time scales, are compatible with state-of-the-art arrays of optical tweezers. Our work shows a highly versatile handle for engineering multi-body interactions of quantum many-body systems in most recent manifestations on Rydberg lattice quantum simulators.