  The probability of observing a large deviation (LD) in the number of
particles in a region $\Lambda$ in a dilute quantum gas contained in a much
larger region $V$ is shown to decay as $\exp[-|\Lambda|\Delta F]$, where $|\L|$
is the volume of $\Lambda$ and $\Delta F$ is the change in the appropriate free
energy density, the same as in classical systems. However, in contrast with the
classical case, where this formula holds at all temperatures and chemical
potentials our proof is restricted to rarefied gases, both for the typical and
observed density, at least for Bose or Fermi systems. The case of Boltzmann
statistics with a bounded repulsive potential can be treated at all
temperatures and densities. Fermions on a lattice in any dimension, or in the
continuum in one dimension, can be treated at all densities and temperatures if
the interaction is small enough (depending on density and temperature),
provided one assumes periodic boundary conditions.
