  We propose a hybrid quantum system where the strong coupling regime can be
achieved between a Rydberg atomic ensemble and propagating surface phonon
polaritons on a piezoelectric superlattice. By exploiting the large electric
dipole moment and long lifetime of Rydberg atoms as well as tightly confined
surface phonon polariton modes, it is possible to achieve a coupling constant
far exceeding the relevant decay rates. The frequency of the surface mode can
be selected so it is resonant with a Rydberg transition by engineering the
piezoelectric superlattice. We describe a way to observe the Rabi splitting
associated with the strong coupling regime under realistic experimental
conditions. The system can be viewed as a new type of optomechanical system.
