Effects of spin-phonon coupling on coherent Rydberg facilitation in a lattice

In recent years, Rydberg atoms have proven themselves as a powerful tool for quantum simulators, one of the reasons being their strong and long-ranged interactions .

One interesting phenomenon resulting from these interactions is Rydberg facilitation, or anti-blockade, where an atom excited to the Rydberg state moves a neighboring atom into resonance with a laser field, thus facilitating a fast excitation cascade in a regular lattice of trapped atoms.

However, along with strong dipolar interactions between Rydberg atoms (spins), come mechanical forces coupling Rydberg atoms to high motional states (phonons) in their respective tweezer traps. For a chain of atoms trapped in tweezer arrays under the facilitation constraint, we numerically and analytically investigate the dynamics of the spin-phonon coupling in the coherent regime of Rydberg facilitation . To this end, we approximate the van-der-Waals interaction potential up to second order.

In particular we investigate how the motional degrees of freedom affect the spreading dynamics of Rydberg excitations. We demonstrate that spin-phonon-coupling in the low-excitation regime leads to Bloch Oscillations of spin excitation chains. In the high-excitation regime, we show that quantum fluctuations of phonons lead to Anderson localization in the spreading dynamics of Rydberg domains.