Density profiles for atomic quantum Hall states

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We analyze density profiles for atomic quantum Hall states, which are expected to form in systems of rotating cold atoms in the high-rotation limit. For a two-dimensional (single-layer) system we predict a density landscape showing plateaus at quantized densities, signaling the formation of incompressible groundstates. For a set-up with parallel, coupled layers, we predict (i) at intermediate values of the inter-layer tunneling: a continuously varying density profile ρ(z) across the layers, showing cusps at specific positions, (ii) at small values for the tunneling, quantum Hall-Mott phases, with individual layers at sharply quantized particle number, and plateaus in the density profile ρ(z).