Spin-Phonon Coupling in a 1D Lattice using Rydberg Facilitation*

Rydberg anti-blockade (facilitation) offers a promising mechanism for realizing robust neutral-atom quantum gates for atoms in tweezer traps. However, concomitant with the strong dipolar interactions between Rydberg atoms (spins) are mechanical forces coupling Rydberg atoms to high motional states (phonons) in the traps. This has so far kept experimental realizations of quantum gates with facilitation out of reach. Recently, Rydberg excitations have been created by coupling to an avoided-crossing potential in an experimental setting. This approximately harmonic potential alters the nature of the spin-phonon coupling and therefore might offer a method of realizing quantum gates.

For a chain of atoms trapped in tweezer arrays under the facilitation constraint, we numerically simulate the dynamics of the spin-phonon coupling using tensor-network approaches and present a simple analytical model which provides a quantitative understanding of the dynamics. In particular we investigate how the motional degrees of freedom affect the spreading dynamics of spin excitations and how correlations between spins and phonons impact the dynamics of the system.