  We propose a method to trap polar molecules with the electrical force induced
by the surface acoustic wave (SAW) on piezoelectric materials. In this
approach, the electrical force is perpendicular to the moving direction of the
polar molecules, and is used to control the positions of trapped polar
molecules in the direction orthogonal to the acoustic transmission. By virtue
of an external electrical force, the SAW-induced electrical field can trap the
polar molecules into single-layer or multi-layer lattices. The arrangement of
molecules can affect the binding energy and localization of the molecule array.
Then the one- or two-dimensional trapped polar molecule arrays can be used to
construct the Bose-Hubbard (BH) model, whose energy and dynamics are affected
by the localizations of the trapped molecules. We find that the phase
transitions between the superfluid and Mott insulator based on trapped polar
molecule BH model can be modulated by the SAW induced electrical potential.
