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We explore the groundstates of a few dipolar bosons in optical lattices withincommensurate filling. The competition of kinetic, potential, and interactionenergies leads to the emergence of a variety of crystal state orders withcharacteristic one- and two-body densities. We probe the transitions betweenthese orders and construct the emergent state diagram as a function of thedipolar interaction strength and the lattice depth. We show that the crystalstate orders can be observed using the full distribution functions of theparticle number extracted from simulated single-shot images.

Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions