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We describe the density profiles of confined atomic Bose gases in thehigh-rotation limit, in single-layer and multi-layer geometries. We show that,in a local density approximation, the density in a single layer shows alandscape of quantized steps due to the formation of incompressible liquids,which are analogous to fractional quantum Hall liquids for a two-dimensionalelectron gas in a strong magnetic field. In a multi-layered set-up we finddifferent phases, depending on the strength of the inter-layer tunneling t. Wediscuss the situation where a vortex lattice in the three-dimensionalcondensate (at large tunneling) undergoes quantum melting at a criticaltunneling $t_{c_1}$. For tunneling well below $t_{c_1}$ one expects weaklycoupled or isolated layers, each exhibiting a landscape of quantum Hallliquids. After expansion, this gives a radial density distribution withcharacteristic features (cusps) that provide experimental signatures of thequantum Hall liquids.Comment: 9 pages, 9 figure

Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries