  We propose a method to realize the Frenkel-Kontorova model using an array of
Rydberg dressed atoms. Our platform can be used to study this model with a
range of realistic interatomic potentials. In particular, we concentrate on two
types of interaction potentials: a springlike potential and a repulsive
long-range potential. We numerically calculate the phase diagram for such
systems and characterize the Aubry-like and commensurate-incommensurate phase
transitions. Experimental realizations of this system that are possible to
achieve using current technology are discussed.
