Non-Classical Spin-Phonon Correlations Induced by Rydberg Facilitation in a Lattice

We investigate the interplay between mechanical forces and the internal-state dynamics of a chain of Rydberg atoms trapped in tweezer arrays under the facilitation constraint. Dipole interactions between Rydberg atoms couple electronic (spin) degrees of freedom with excited motional (phonon) states. We show that this interaction leads to highly correlated and non-classical phonon states in the form of squeezed center of mass position states of the Rydberg atoms. Coupling with either a normal or an inverted Lennard-Jones-type potential, resulting from an avoided crossing of Rydberg potential curves, leads to in-phase or out-of-phase correlated oscillations in the atom positions respectively. Furthermore, the growth dynamics of a finite cluster of excited Rydberg atoms can be mapped to the dynamics of a single particle in a semi-infinite lattice subject to a linear potential gradient caused by spin-phonon interactions. This results in Bloch oscillations in the spin cluster size, which in turn localize spin excitations in the system.