A gas of ultracold ${}^6$Li atoms (effective spin 1/2) confined to an elongated trap with one-dimensional properties is a candidate to display three different phases: (i) fermions bound in Cooper-pair-like states, (ii) unbound spin-polarized particles, and (iii) a mixed phase in which Cooper bound states and unpaired particles coexist. It is of great interest to extend these studies to fermionic atoms with higher spin, e.g., for neutral ${}^{40}$K, ${}^{43}$Ca, ${}^{87}$Sr, or ${}^{173}$Yb atoms. Within the grand-canonical ensemble, we investigated the $\mu$ versus $H$ phase diagram ($\mu$ is the chemical potential and $H$ the external magnetic field) for $S=3/2,...,9/2$ for the ground state using the exact Bethe ansatz solution of the one-dimensional Fermi gas with an attractive $\delta$-function interaction potential. There are $N=2S+1$ fundamental states: the particles can be either unpaired or clustered in bound states of 2, 3, $\cdots$, $2S$, and $2S+1$ fermions. The rich phase diagram consists of these $N$ states and various mixed phases in which combinations of the fundamental states coexist. Bound states of $N$ fermions are not favorable in high magnetic fields, but always present if the field is low. For $S=3/2,$ possible scenarios for phase separation are explored within the local density approximation. For $S=3/2,$ the phase diagram for the superposition of a Zeeman and a quadrupolar splitting is also discussed.

• Received 11 April 2011

DOI:https://doi.org/10.1103/PhysRevB.85.024535