  We study shot (counting) noise of the amplitude of interference between
independent atomic systems. In particular, for the two interfering systems the
variance of the fringe amplitude decreases as the inverse power of the number
of particles per system with the coefficient being a non-universal number. This
number depends on the details of the initial state of each system so that the
shot noise measurements can be used to distinguish between such states. We
explicitly evaluate this coefficient for the two cases of the interference
between bosons in number states and in broken symmetry states. We generalize
our analysis to the interference of multiple independent atomic systems. We
show that the variance of the interference contrast vanishes as the inverse
power of the number of the interfering systems. This result, implying high
signal to noise ratio in the interference experiments, holds both for bosons
and for fermions.
