  In ultracold gases many experiments use atom imaging as a basic observable.
The resulting image is averaged over a number of realizations and mostly only
this average is used. Only recently the noise has been measured to extract
physical information. In the present paper we investigate the quantum noise
arising in these gases at zero temperature. We restrict ourselves to the
homogeneous situation and study the fluctuations in particle number found
within a given volume in the gas, and more specifically inside a sphere of
radius $R$. We show that zero-temperature fluctuations are not extensive and
the leading term scales with sphere radius $R$ as $R^2\ln R$ (or $\ln R$) in
three- (or one-) dimensional systems. We calculate systematically the next term
beyond this leading order. We consider first the generic case of a compressible
superfluid. Then we investigate the whole Bose-Einstein-condensation (BEC)-BCS
crossover crossover, and in particular the limiting cases of the weakly
interacting Bose gas and of the free Fermi gas.
