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

TL;DR

This paper develops exact algebraic wavefunctions for a few strongly correlated ultracold fermionic atoms in rapid rotation, revealing their Wigner-molecular structures and enabling precise spectral analysis beyond previous methods.

Contribution

It introduces a novel theoretical framework combining numerical diagonalization with symbolic processing to derive exact spinful wavefunctions for rotating ultracold fermions.

Findings

Exact algebraic wavefunctions match numerical results precisely.

Wavefunctions reveal formation of rotating and vibrating Wigner molecules.

Method extends beyond limitations of previous Jastrow-type approaches.

Abstract

Exploring strongly correlated spinful states of few fermionic ultracold atoms in a rapidly rotating trap, an example of which was recently realized for two fermionic $^6$Li atoms in an optical tweezer, we derive analytical (algebraic) total-spin-eigenstate wavefunctions 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 wavefunctions (for two and three spinful $^6$Li atoms) reproduce precisely the corresponding numerical FCI results, and they 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