  We discuss the issue of measuring the mean position (center-of-mass) of a
group of bosonic or fermionic quantum particles, including particle number
fluctuations. We introduce a standard quantum limit for these measurements at
ultra-low temperatures, and discuss this limit in the context of both photons
and ultra-cold atoms. In the case of fermions, we present evidence that the
Pauli exclusion principle has a strongly beneficial effect, giving rise to a
1/N scaling in the position standard-deviation -- as opposed to a $1/\sqrt{N}$
scaling for bosons. The difference between the actual mean-position fluctuation
and this limit is evidence for quantum wave-packet spreading in the
center-of-mass. This macroscopic quantum effect cannot be readily observed for
non-interacting particles, due to classical pulse broadening. For this reason,
we also study the evolution of photonic and matter-wave solitons, where
classical dispersion is suppressed. In the photonic case, we show that the
intrinsic quantum diffusion of the mean position can contribute significantly
to uncertainties in soliton pulse arrival times. We also discuss ways in which
the relatively long lifetimes of attractive bosons in matter-wave solitons may
be used to demonstrate quantum interference between massive objects composed of
thousands of particles.
