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The fractional quantum Hall effect (FQHE) is theoretically investigated, withnumerical and algebraic approaches, in assemblies of a few spinful ultracoldneutral fermionic atoms, interacting via repulsive contact potentials andconfined in a single rapidly rotating two-dimensional harmonic trap. Goingbeyond the commonly used second-order correlations in the real configurationspace, the methodology in this paper will assist the analysis of experimentalobservations by providing benchmark results for $N$-body spin-unresolved, aswell as spin-resolved, momentum correlations measurable in time-of-flightexperiments with individual particle detection. Our analysis shows that thefew-body lowest-Landau-level (LLL) states with good magic angular momentaexhibit inherent ordered quantum structures in the $N$-body correlations,similar to those associated with rotating Wigner molecules (WMs), familiar fromthe field of semiconductor quantum dots under high magnetic fields. Theapplication of a small perturbing stirring potential induces, at the ensuingavoided crossings, formation of symmetry broken states exhibiting orderedpolygonal-ring structures, explicitly manifest in the single-particle densityprofile of the trapped particles. Away from the crossings, an LLL stateobtained from exact diagonalization of the microscopic Hamiltonian, found to bewell-described by a (1,1,1) Halperin two-component variational wavefunction,represents also a spinful rotating WM. Analysis of the calculated LLLwavefunction enables a two-dimensional generalization of the Girardeauone-dimensional 'fermionization' scheme, originally invoked for mapping ofbosonic-type wave functions to those of spinless fermions.

physical review. a/physical review, a

Fractional quantum Hall physics and higher-order momentum correlations  in a few spinful fermionic contact-interacting ultracold atoms in rotating  traps