Pairing in SU(6) $\times$ SU(2) one-dimensional fermionic clusters

Abstract

We present diffusion Monte Carlo (DMC) calculations on the behavior of a mixture of $^{173}$Yb and $^{171}$Yb fermionic isotopes in a one-dimensional environment. The interaction parameters between species were modeled by delta potentials, whose strengths were taken from their experimental scattering lengths and varied by changing the transversal confinement. This implies a repulsive interaction for the $^{173}$Yb-$^{173}$Yb pair, a strong attractive one for the $^{173}$Yb-$^{171}$Yb set and a weak attraction between $^{171}$Yb-$^{171}$Yb atoms. Those arrangements were described by a corrected geminal multiplied by the appropriate set of Jastrow functions. We found that, for the same number of strong attractive pairs, the width of the cluster decreases when the number of fermionic species increases, the narrower cluster being the one that includes a mixture of six $^{173}$Yb species and two $^{171}$Yb spin types.