Quantum phases for bosons in a magnetic lattice with a harmonic trap

The phase diagram of ultracold bosons in a 2D optical lattice subjected to a uniform magnetic flux is studied by the inhomogeneous Gutzwiller variational method. With a harmonic external potential, the density profile exhibits wedding-cake shape and the Mott phase forms a series of circular platforms with integer fillings. There are annular rings of superfluid between these platforms. We identify a lot of phases, including the unicirculation phase, the Meissner phase, the vortex phase, the reversed current phase and the vortex superfluid phase, by examining the super-currents. The circular chiral currents of the reversed current phase are opposite to other phases in annular superfluid and we analyzed the transitions between different phases. (paper)