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

We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t(c1). For tunneling well below t(c1) one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids.