Influence of the trap shape on the superfluid-Mott transition in   ultracold atomic gases
  The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid-Mott transition difficult. Studying alternative trapping potentials which are experimentally realizable and have a flatter center, we find that the transition can be better resolved, but at the cost of a more difficult tuning of the particle filling. When mapping out the phase diagram using local probes and the local density approximation we find that the smoother gradient of the parabolic trap is advantageous. 
Ping Nang Ma, Kai Yu Yang, Lode Pollet, J. V. Porto, Matthias Troyer,   Fu Chun Zhang