Long-range transverse Ising model built with dipolar condensates in two-well arrays

Dipolar Bose-Einstein condensates in an array of double-well potentials realize an effective transverse Ising model with peculiar inter-layer interactions, that may result under proper conditions in an anomalous first-order ferromagnetic-antiferromagnetic phase transition, and nontrivial phases due to frustration. The considered setup as well allows the study of Kibble-Zurek defect formation, whose kink statistics follows that expected from the universality class of the mean-field transverse Ising model in 1D. Furthermore, random occupation of each layer of the stack leads to random effective Ising interactions and generation of local transverse fields, thus allowing the study of Anderson-like localization of imbalance perturbations in the two-well stack under controllable conditions.