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Phase transitions and their associated crossovers are imprinted in thebehavior of fluctuations. Motivated by recent experiments on ultracold atoms inoptical lattices, we compute the thermodynamic density fluctuations $\deltaN^2$ of the two-dimensional fermionic Hubbard model with plaquette cellulardynamical mean-field theory. To understand the length scale of thesefluctuations, we separate the local from the nonlocal contributions to $\deltaN^2$. We determine the effects of particle statistics, interaction strength$U$, temperature $T$ and density $n$. At high temperature, our theoreticalframework reproduces the experimental observations in the doping-drivencrossover regime between metal and Mott insulator. At low temperature, there isan increase of thermodynamic density fluctuations, analog to criticalopalescence, accompanied by a surprising reduction of the absolute value oftheir nonlocal contributions. This is a precursory sign of an underlying phasetransition between a pseudogap phase and a metallic phase in doped Mottinsulators, which should play an important role in the cuprate high-temperaturesuperconductors. Predictions for ultracold atom experiments are made.

Critical Opalescence across the Doping Driven Mott Transition in Optical Lattices of Ultracold Atoms