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

TL;DR

This paper investigates few-body resonances in small unequal-mass two-component quantum systems with infinite interspecies scattering length, revealing specific mass ratios where resonances occur and discussing their potential experimental observability.

Contribution

It provides a detailed analysis of non-universal few-body resonances in unequal-mass systems without Efimov physics, identifying resonance conditions and structural properties.

Findings

Resonances at mass ratios 12.314(2) and 10.4(2) for (2,1) and (3,1) systems

Large size of systems on resonance suggests long lifetimes

Feasibility of experimental probing with current technology

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 [D. Blume and K. M. Daily, arXiv:1006.5002] 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 non-universal 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 non-perturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio $\kappa$, 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 $\kappa = 12.314(2)$ and 10.4(2), respectively. The three- and four-particle systems on resonance are found to be large. This suggests that the corresponding wave function has relatively small overlap with deeply-bound dimers, trimers or larger clusters and that the three- and four-body systems on resonance have a comparatively long lifetime. Thus, it seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.