  We measure the population distribution in one of the atomic twin beams
generated by four-wave mixing in an optical lattice.
  Although the produced two-mode squeezed vacuum state is pure, each individual
mode is described as a statistical mixture.
  We confirm the prediction that the particle number follows an exponential
distribution when only one spatio-temporal mode is selected.
  We also show that this distribution accounts well for the contrast of an
atomic Hong--Ou--Mandel experiment.
  These experiments constitute an important validation of our twin beam source
in view of a future test of a Bell inequalities.
