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

• URL: http://arxiv.org/abs/2006.09602v2
• Date: Thu, 15 Oct 2020 17:35:12 GMT
• Title: Fractional quantum Hall physics and higher-order momentum correlations in a few spinful fermionic contact-interacting ultracold atoms in rotating traps
• Authors: Constantine Yannouleas, Uzi Landman
• Abstract summary: This paper provides benchmark results for $N$-body spin-unresolved, as well as spin-resolved, momentum correlations measurable in time-of-flight experiments with individual particle detection. The application of a small perturbing stirring potential induces, at the ensuing avoided crossings, formation of symmetry broken states exhibiting ordered polygonal-ring structures. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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