Few-body resonances of unequal-mass systems with infinite interspecies two-bodys-wave scattering length

Abstract

Two-component Fermi and Bose gases with infinitely large interspecies $s$-wave scattering length ${a}_{s}$ exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [Phys. Rev. Lett. 105, 170403 (2010)] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite ${a}_{s}$ in the regime where three-body Efimov physics is absent. We report on nonuniversal few-body resonances. Just like with two-body systems on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a nonperturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio $\ensuremath{\kappa}$, and the numbers ${N}_{1}$ and ${N}_{2}$ of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the $({N}_{1},{N}_{2})=(2,1)$ and $(3,1)$ systems exhibit three-body and four-body resonances at mass ratios $\ensuremath{\kappa}=12.314(2)$ and $10.4(2)$, respectively. The three- and four-particle systems on resonance are found to be large. It seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.