We explore the ground-state properties of bosons with dipole-dipole
interactions in a one-dimensional optical lattice. Remarkably, a
crystallization process happens for strong dipolar interactions. Herein, we
provide a detailed characterization and a way to measure the resulting crystal
phase. Using the eigenvalues of the reduced one-body density matrix we define
an order parameter that yields a phase diagram in agreement with an analysis of
the density and two-body density. We demonstrate that the phase diagram can be
detected experimentally using the variance of single-shot measurements.Comment: 6 pages, 3 figures. Supplementary Information included. Software
available at http://ultracold.org
