  We investigate pair correlations in trapped fermion and boson gases as a
means to probe the quantum states producing the density fluctuations. We point
out that "opposite sign correlations" (meaning pair correlations that are
positive for fermions and negative for bosons) unambiguously indicate that the
quantum many-particle state cannot be "free." In particular, a system of
fermions that exhibits positive pair correlations cannot be described by any
Slater determinant wavefunction. This insight may help one to interpret results
of current experiments on ultracold atomic gases.
