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
Phys. Rev. A 111, 063309 – Published 13 June, 2025
DOI: https://doi.org/10.1103/6hst-g33w
Abstract
Exploring strongly correlated spinful states of a few fermionic ultracold atoms in a rapidly rotating trap, an example of which was recently realized for two fermionic atoms in an optical tweezer, we derive analytical (algebraic) total-spin-eigenstate wave functions through the development and employment of a theoretical platform that integrates exact numerical diagonalization (full configuration interaction, FCI) with symbolic language processing. For such rapid rotations, where the atoms occupy the lowest Landau level (LLL), the obtained algebraic expressions can address the full LLL spectrum in all its complexity, demonstrating that their spatial, spectral, and spin characteristics manifest formation of collectively rotating and vibrating Wigner molecules. The explicitly exhibited analytic wave functions (for two and three spinful atoms) reproduce precisely the corresponding numerical FCI results and are shown to reach beyond the limited range of applicability of previous Jastrow-type treatments. These results, and their extension to bosonic systems, provide the impetus and analysis tools for future experimental and theoretical simulations of larger mesoscopic systems.
