We explore one-dimensional samples of ultracold polar molecules with attractive dipole-dipole interactions and show the existence of a repulsive barrier caused by a strong quadrupole interaction between molecules. This barrier can stabilize a gas of ultracold KRb molecules and even lead to long-range wells supporting bound states between the molecules. The properties of these wells can be controlled by external electric fields, allowing the formation of long polymerlike chains of KRb and studies of quantum phase transitions by varying the effective interaction between molecules. We discuss the generalization of those results to other systems.
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