Entanglement of mechanical oscillators mediated by a Rydberg tweezer chain

Mechanical systems provide a unique test bed for studying quantum phenomena at macroscopic length scales. However, realizing quantum states that feature quantum correlations among macroscopic mechanical objects remains an experimental challenge. Here, we propose a quantum system in which two micro-electromechanical oscillators interact through a chain of Rydberg atoms confined in optical tweezers. We demonstrate that the coherent dynamics of the system generate entanglement between the oscillators. Furthermore, we utilize the tunability of the radiative decay of the Rydberg atoms for dissipative entanglement generation. Our results highlight the potential to exploit the flexibility and tunability of Rydberg atom chains to generate nonclassical correlations between distant mechanical oscillators.