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Minimization of the energy was carried out numerically for given areal density by allowing the positions of the planes to vary with respect to one another within the external potential and by varying the lattice structure within the planes. We made the simplifying assumption, which was consistent with the experimental observations, that the lattice structure of each plane was identical. The areal density of the planar OCP is a control parameter that, when varied, leads to transitions in both the number and lattice structure of the planes. This theory focuses on the minimum potential energy states while neglecting finite temperature effects that may be important (particularly effects that are near the continuous phase transitions where large structural fluctuations may occur).
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This manuscript is a work of the U.S. government; it is not subject to U.S. copyright. This research was supported by the Office of Naval Research and NSF (D.H.E.D.). We thank B. King, R. J. Rafac, J. P. Schiffer, and D. J. Wineland for useful comments and B. M. Jelenković and J. N. Tan for technical assistance.
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