Novel Ferromagnetic Domains and Quantum Criticality with Bose Condensates in a Shaken Optical Lattice

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While atoms have been long recognized as the building blocks of the world we see and the environment we live in, their behavior at low temperatures has never ceased to surprise us. Examples include superfluids that flow without friction and quantum magnetic materials that permit read, write and storage of ample information. A recent work led by the principal investigator showed that both superfluidity and ferromagnetism (the type of magnetism in bar magnets) manifest simultaneously in atoms when shaken back and forth by laser beams, like ping-pong balls riding the ripples on a lake. The intriguing dynamics of magnetic domains observed in the atomic superfluids suggests new strategies to efficiently store and process information in the quantum regime. The major science goal of this project is to simulate and study a new type of 4-pole magnet in a two-dimensional lattice, which promises much richer properties than the 2-pole (south and north pole) magnetism in conventional materials. The science program is complimented by an extensive outreach effort under the S.M.A.R.T. (Science, Mathematics, And Research Training) project. The proposed 4-pole magnetic phase will arise when an atomic superfluid is transferred into a two-dimensional shaken optical lattice, generated by overlapping two perpendicular optical standing waves. When the shaking amplitude is carefully tuned above a critical value, the superfluid is anticipated to split into 4 poles with ferromagnetic interactions. The formation of the 4-pole domain will be detected and studied by direct in situ imaging of the atomic sample. Compared to the conventional 2-pole magnets, the 4-pole magnets offer novel domain and vertex structures and are uniquely related to the four-color theorem in graph theory and the Potts model of statistical physics. Furthermore the phase transition into the ferromagnetic phase is associated with a variety of quantum phenomena, including Rashba superfluids, the Berezinskii-Kosterlitz-Thouless transition, and the Kibble-Zurek mechanism. Exploration of this quantum physics may have both academic and practical payoffs, including the development of a theoretical framework to understand quantum critical dynamics, simulations of N-pole ferromagnetic magnets, fabrication of programmable magnetic materials, and potentially even quantum information storage and processing.