Imaging of critical correlations in optical lattices and atomic traps

We consider critical space-time correlations in trapped utracold atoms and propose a method for their detection by the interference with a reference Bose-Einstein condensate. Important information about universal properties can be obtained despite nonuniformity and small sizes of atomic clouds. The advantage of this method is that the correlation properties of the interference pattern are robust with respect to expansion and are not, practically, affected by the microscopic structure of the underlying lattice including structural disorder. The nondestructive scheme allows measuring the space-time correlators of arbitrary order.