  Recently developed techniques allow for simultaneous measurements of the
positions of all ultra cold atoms in a trap with high resolution. Each such
single shot experiment detects one element of the quantum ensemble formed by
the cloud of atoms. Repeated single shot measurements can be used to determine
all correlations between particle positions as opposed to standard measurements
that determine particle density or two-particle correlations only. In this
paper we discuss the possible outcomes of such single shot measurements in case
of cloud of ultra-cold non-interacting Fermi atoms. We show that the Pauli
exclusion principle alone leads to correlations between particle positions that
originate from unexpected spatial structures formed by the atoms.
