Density profiles for atomic quantum Hall states

Abstract

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 $ρ(z)$.