  We theoretically investigate the manipulation of the motional states of
trapped ground-state atoms using Rydberg dressing via nonresonant laser fields.
The forces resulting from Rydberg-state interaction between dressed neighboring
atoms in an array of microtraps or an optical lattice can strongly couple their
motion. We show that intensity modulation of the dressing field allows to
squeeze the relative motion of a pair of atoms and generate non-classical
mechanical states. Extending this pairwise scheme to one-dimensional chains
provides flexible control over the mechanical degrees of freedom of the whole
system. We illustrate our findings with protocols to manipulate all motional
degrees of freedom of a pair of atoms and create entangled states. We also
present a method to transfer non-classical correlations along an atomic chain
of nontrivial length. The long-lived nature of motional states, together with
the high tunability of Rydberg dressing, makes our proposal feasible for
current experimental setups.
