  Critical behavior developed near a quantum phase transition, interesting in
its own right, offers exciting opportunities to explore the universality of
strongly-correlated systems near the ground state. Cold atoms in optical
lattices, in particular, represent a paradigmatic system, for which the quantum
phase transition between the superfluid and Mott insulator states can be
externally induced by tuning the microscopic parameters. In this paper, we
describe our approach to study quantum criticality of cesium atoms in a
two-dimensional lattice based on in situ density measurements. Our research
agenda involves testing critical scaling of thermodynamic observables and
extracting transport properties in the quantum critical regime. We present and
discuss experimental progress on both fronts. In particular, the thermodynamic
measurement suggests that the equation of state near the critical point follows
the predicted scaling law at low temperatures.
