Unbalanced droplets of one-dimensional mixtures of fermions

By means of a diffusion Monte Carlo technique, we study one-dimensional unbalanced mixtures of fermionic ytterbium atoms ($^{173}\mathrm{Yb}$ and $^{171}\mathrm{Yb}$). This means clusters in which the total number of $^{173}\mathrm{Yb}$ particles is different from the sum of all the atoms belonging to the $^{171}\mathrm{Yb}$ isotope. Our aim will be to check the possibility of having self-bound arrangements beyond the balanced compositions reported in previous literature rather than exploring all the situations in which that could be possible. In that vein, we focused mainly on mixtures in which the atoms belonging to one isotope are spin polarized, while the spins of the particles in the other isotope are evenly distributed in two sets. What we found was that, even though self-bound droplets are possible for different compositions, the most stable ones are clusters with a slight excess of attractively interacting $^{171}\mathrm{Yb}$ particles with different spins with respect to the number of spin-polarized $^{173}\mathrm{Yb}$ atoms. Clusters in which the number of repulsively interacting unequal-spin $^{173}\mathrm{Yb}$ atoms are in excess with respect to the spin-polarized $^{171}\mathrm{Yb}$ particles have a very narrow stability range.