We investigate the effect of dipolar interactions in one-dimensional systems in connection with the possibility of observing exotic many-body effects with trapped atomic and molecular dipolar gases. By combining analytical and numerical methods, we s
how how the competition between short- and long-range interactions gives rise to frustrating effects which lead to the stabilization of spontaneously dimerized phases characterized by a bond-ordering. This genuine quantum order is sharply distinguished from Mott and spin-density wave phases, and can be unambiguously probed by measuring non local order parameters in-situ imaging techniques.
