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. An important information about universal properties can be obtained despite non-uniformity 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 microscopic structure of underlying lattice including structural disorder. The non-destructive scheme allows measuring the space-time correlators of arbitrary order.