  We propose and analyze an electrostatic-optical nano-scale trap for cold
diatomic polar molecules. The main ingredient of our proposal is an
square-array of ferroelectric nano-rods {with alternating polarization}. We
show that, in contrast to electrostatic traps using the linear Stark effect, a
quadratic Stark potential supports long-lived trapped states. The molecules are
kept at a fixed height from the nano-rods by a standing-wave optical dipole
trap. For the molecules and materials considered, we find that nano-traps with
trap frequency up to 1MHz, ground-state width $\sim20$nm with lattice
periodicity of $\sim 200$nm. Analyzing the loss mechanisms due to
non-adiabaticity, surface-induced radiative transitions, and laser-induced
transitions, we show the existence of trapped states with life-time $\sim 1$s,
competitive with current traps created via optical mechanisms. As an
application we extend our discussion to an 1D array of nano-traps to simulate
of a long-range spin Hamiltonian in our structure.
