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

Abstract

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.

arXiv comment33 pages with 12 color figures (includes Supplemental Material and MATHEMATICA scripts). Extensive clarifications and additions. Accepted for publication in Physical Review A. For related papers, see https://sites.gatech.edu/cyannouleas

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Cited by in corpus (4)

• Quantum Wigner molecules in moiré materials
• Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap
• Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior