Crystalline phases of laser-driven dipolar Bose-Einstein condensates

Although crystallization is a ubiquitous phenomenon in nature, crystal formation and melting still remain fascinating processes with several open questions yet to be addressed. In this work we study the emergent crystallization of a laser-driven dipolar Bose-Einstein condensate due to the interplay between long-range magnetic and effectively infinite-range light-induced interactions. The competition between these two interactions results in a collective excitation spectrum with two-roton minima that introduce two different length scales at which crystalline order can emerge. In addition to the formation of regular crystals with simple periodic patterns due to the softening of one of the rotons, we find that both rotons can also soften simultaneously, resulting in the formation of exotic, complex periodic, or aperiodic density patterns. We also demonstrate dynamic state-preparation schemes for achieving all the crystalline ground states found for experimentally relevant and feasible parameter regimes.