Universal clusters as building blocks of stable quantum matter

We present an exploratory study that suggests that Efimov physics, a leading research theme in few-body quantum physics, can also induce stable many-body ground states whose building blocks are universal clusters. We identify a range of parameters in a mass-and-density-imbalanced two-species fermionic mixture for which the ground state is a gas of Efimov-related universal trimers. An explicit calculation of the trimer-trimer interaction reveals that the trimer phase is an SU(3) Fermi liquid stable against recombination losses. We propose to experimentally observe this phase in a fermionic ${}^6\text{Li}\text{−}{}^{53}\text{Cr}$ mixture.

Figure 1

The number of $\uparrow$ $(n_{\uparrow })$ and $\downarrow$ $\left(n_{\downarrow }\right)$ fermions, dimers $n_{\dim }$, and trimers $n_{\mathrm{tri}}$ as a function of the population imbalance $n_{\uparrow }/n_{\mathrm{tot}}$, where $n_{\mathrm{tot}}=n_{\uparrow }+n_{\downarrow }$ is the total fermion density. These results are strictly valid in the dilute limit that neglects completely interactions among fermions, dimers, and trimers. Moreover for fermionic ground states we also neglect the effect of a finite Fermi pressure. In this paper, we focus in the region around $n_{\uparrow }/n_{\mathrm{tot}}=2/3$, where the ground state is a superposition of universal trimers.

Figure 2

(a), (b) Trimer-trimer potential, in units of $\hslash /2m{a}^2$ with $m$ the mass of the light particle, calculated with the Born-Oppenheimer approximation for various configurations illustrated in (c)–(h). From (c) top (in the large-$R/a$ limit) red curve to (h) bottom cyan (light gray in gray scale) curve. The distance between the heavy particles is taken to be $q=1.6a$. The trimer-trimer interaction is repulsive at large distance for all configurations. It decays exponentially with a decay constant very similar to that of the square of the dimer wave function [black dashed line in (b)] corresponding to a light particle around a heavy particle.

Figure 3

(a) Trimer-trimer potential for $m_{\uparrow }/m_{\downarrow }=9$ calculated with the resonating group method, where ${\mu }_6=m_{\downarrow }/2+m_{\uparrow }$ is the reduced mass between the trimers. It is repulsive for any trimer-trimer separation $R$ and azimuthal angle $\theta$ between the trimers measured from the quantization axis of the trimer internal states. (b) Trimer-trimer scattering length $a_{F=1}^{tt}$ as a function of mass ratio calculated with the RGM method. It is always positive and decreases as the mass ratio increases. This is expected as the trimers are more tightly bound for larger mass ratio and therefore their cross section is smaller. We note that, strictly speaking, our results are only applicable for mass ratios $\le 12.9$. For larger mass ratios an additional universal trimer state becomes available and the calculation of the scattering length becomes much more involved.