Bethe-ansatz analysis of near-resonant two-component systems in one dimension

We introduce a type of model of two-component systems in one dimension that can be analyzed by the Bethe-ansatz approach. The interspecies interactions are tunable via Feshbach resonant interactions, and the Yang-Baxter equation for exact solvability is fulfilled by fine-tuning the resonant energies. Although the strict exact solvability beyond the level of two-body scatterings would require extra singular counterterms, the models introduced here can still be well described by the Bethe ansatz for relatively small densities. The resulting systems can be described by introducing intraspecies repulsive and interspecies attractive couplings c(1) and c(2). This kind of system admits two types of interesting solutions: In the regime with c(1) > c(2), the ground state is a Fermi sea of two-strings, where the Fermi momentum Q is constrained to be smaller than a certain value Q*, and it provides an ideal scenario to realize the BCS-BEC crossover (from weakly attractive atoms to weakly repulsive molecules) in one dimension. In the opposite regime with c(1) < c(2), the ground state is a single bright soliton even for fermionic atoms, which reveals itself as an embedded string solution.