Geometric Frustration in an Optical Superlattice

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The structure of many materials is determined by how the constituents of the material obey the many constraints that are established by microscopic physical principles. For example, stable crystalline structures are those that are constrained to minimize the pairwise interactions between the atoms or molecules forming the crystal. Similarly, in magnetic materials, the magnetic moments of electrons that are localized on neighboring atoms may lower their energy either by aligning in the same or in opposite orientations. In some cases, there is no trivial way in which to satisfy all the energetic constraints within a system, and so the formation of any simple configuration of the system -- e.g. of magnetic moments within a crystalline structure -- is precluded. This phenomenon is known as frustration. The question of whether some sort of predictable order is established in frustrated systems, and, if so, what is the character of that order, are both major open questions in physics. The answer to these questions has relevance to the design of new materials and the application of such materials to information technology and other uses.In this project, the physics of frustrated materials will be explored using cold atoms that are trapped within geometric patterns -- such as the two-dimensional kagome lattice -- that lead to a high degree of frustration. The effects of this frustration on phase transitions and on transport will be investigated. The system chosen provides a clean realization of geometric frustration, free of the structural defects that influence solid-state realizations of similar systems. Thus, the experimental findings may provide clear answers to vexing questions regarding geometric frustration.