Fractional quantum Hall physics and higher-order momentum correlations in a few spinful fermionic contact-interacting ultracold atoms in rotating traps
Constantine Yannouleas, Uzi Landman
备注：
33 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
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.
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
Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin $0 \leq S \leq N/2$ in the neighborhood of the $ν=1$ filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical prediction…
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Pairing of mobile charge carriers in doped antiferromagnets plays a key role in the emergence of unconventional superconductivity. In these strongly correlated materials, the pairing mechanism is often assumed to be mediated by magnetic correlations, in contrast to phonon-mediated interactions in conventional superconductors. A precise understanding of the underlying mechanism in real materials is, however, still lacking, and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies established the emergence of binding among dopants in ladder syste…
It is now possible to study experimentally the combined effect of disorder and interactions in cold atom physics. Motivated by these developments we investigate the dynamics around the metal-insulator transition (MIT) in a one-dimensional (1D) Fermi gas with short-range interactions in a quasiperiodic potential by the time-dependent density-matrix renormalization group (tDMRG) technique. By tuning disorder and interactions we study the MIT from the weakly to the strongly interacting limit. The MIT is not universal as time evolution, well described by a process of anomalous diffusion, depends q…
