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We report results of quantum Monte Carlo simulations in the canonical and thegrand-canonical ensemble of the two- and three-dimensional Bose-Hubbard modelwith quadratic and quartic confining potentials. The quantum criticality of thesuperfluid-Mott insulator transition is investigated both on the boundary layerseparating the two coexisting phases and at the center of the traps where theMott-insulating phase is first established. Recent simulations of systems inquadratic traps have shown that the transition is not in the critical regimedue to the finite gradient of the confining potential and that criticalfluctuations are suppressed. In addition, it has been shown that quantumcritical behavior is recovered in flat confining potentials as they approachthe uniform regime. Our results show that quartic traps display a behaviorsimilar to quadratic ones, yet locally at the center of the traps the bulktransition has enhanced critical fluctuations in comparison to the quadraticcase. Therefore quartic traps provide a better prerequisite for theexperimental observation of true quantum criticality of ultracold bosonic atomsin optical lattices.

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps