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We study properties of the lowest energy states at non-zero total momentum(yrast states) of the Hubbard model for spin-1/2 fermions in the quantum ringconfiguration with attractive on-site interaction at low density. In theone-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz,while for the crossover into the 2D regime we use theFull-Configuration-Interaction Quantum Monte-Carlo method (FCIQMC) to obtainthe yrast states for the spin-balanced Fermi system. We show how the yrastexcitation spectrum changes from the 1D to the 2D regime and how pairingaffects the yrast spectra. We also find signatures of fragmented condensationfor certain yrast states usually associated with dark solitons.

Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings