  The fractional quantum Hall effect (FQHE) is theoretically investigated, with
numerical and algebraic approaches, in assemblies of a few spinful ultracold
neutral fermionic atoms, interacting via repulsive contact potentials and
confined in a single rapidly rotating two-dimensional harmonic trap. Going
beyond the commonly used second-order correlations in the real configuration
space, the methodology in this paper will assist the analysis of experimental
observations by providing benchmark results for $N$-body spin-unresolved, as
well as spin-resolved, momentum correlations measurable in time-of-flight
experiments with individual particle detection. Our analysis shows that the
few-body lowest-Landau-level (LLL) states with good magic angular momenta
exhibit inherent ordered quantum structures in the $N$-body correlations,
similar to those associated with rotating Wigner molecules (WMs), familiar from
the field of semiconductor quantum dots under high magnetic fields. The
application of a small perturbing stirring potential induces, at the ensuing
avoided crossings, formation of symmetry broken states exhibiting ordered
polygonal-ring structures, explicitly manifest in the single-particle density
profile of the trapped particles. Away from the crossings, an LLL state
obtained from exact diagonalization of the microscopic Hamiltonian, found to be
well-described by a (1,1,1) Halperin two-component variational wavefunction,
represents also a spinful rotating WM. Analysis of the calculated LLL
wavefunction enables a two-dimensional generalization of the Girardeau
one-dimensional 'fermionization' scheme, originally invoked for mapping of
bosonic-type wave functions to those of spinless fermions.
