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Localization and Fractionalization in a Chain of Rotating Atomic Gases

We describe the phase diagram and thermodynamic properties of a chain of axially-tunnel-coupled fractional quantum Hall systems realized by rotating a series of optical dipole traps about their center. We demonstrate not only a experimentally feasible pathway to a state describable as a Mott-insulator of composite bosons, but also describe the nature of the coherent states at higher tunnel coupling strength, and identify a series of new superfluid phases with rich behavior. The phase diagram directly reveals not only characteristic features of the few-body systems, including the effective mass of composite particle- and hole-like excitations and their interactions, but emergent properties of the chain also reveal a fundamental mapping between the adiabatic dynamics of two dimensional systems governed by particle braiding and the hydrostatic response of the gas in the conducting phases.