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Physical Review A

Pairing in SU(6) × SU(2) one-dimensional fermionic clusters

M. C. Gordillo

Published Aug 31, 2020• 4 citations
Publisher

Abstract

We present diffusion Monte Carlo calculations on the behavior of a mixture of $^{173}\mathrm{Yb}$ and $^{171}\mathrm{Yb}$ fermionic isotopes in a one-dimensional environment. The interaction parameters between species were modeled by $\ensuremath{\delta}$ potentials, whose strengths were taken from their experimental scattering lengths and varied by changing the transversal confinement. This implies a repulsive interaction for the $^{173}\mathrm{Yb}\ensuremath{-}^{173}\mathrm{Yb}$ pair, a strong attractive one for the $^{173}\mathrm{Yb}\ensuremath{-}^{171}\mathrm{Yb}$ set, and a weak attraction between $^{171}\mathrm{Yb}\ensuremath{-}^{171}\mathrm{Yb}$ 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 $^{173}\mathrm{Yb}$ species and two $^{171}\mathrm{Yb}$ spin types.

DOI
10.1103/physreva.102.023335

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We present diffusion Monte Carlo calculations on the behavior of a mixture of 173Yb^{173}\mathrm{Yb}173Yb and 171Yb^{171}\mathrm{Yb}171Yb fermionic isotopes in a one-dimensional environment. The interaction parameters between species were modeled by \ensuremathδ\ensuremath{\delta}\ensuremathδ potentials, whose strengths were taken from their experimental scattering lengths and varied by changing the transversal confinement. This implies a repulsive interaction for the 173Yb\ensuremath−173Yb^{173}\mathrm{Yb}\ensuremath{-}^{173}\mathrm{Yb}173Yb\ensuremath−173Yb pair, a strong attractive one for the 173Yb\ensuremath−171Yb^{173}\mathrm{Yb}\ensuremath{-}^{171}\mathrm{Yb}173Yb\ensuremath−171Yb set, and a weak attraction between 171Yb\ensuremath−171Yb^{171}\mathrm{Yb}\ensuremath{-}^{171}\mathrm{Yb}171Yb\ensuremath−171Yb 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 173Yb^{173}\mathrm{Yb}173Yb species and two 171Yb^{171}\mathrm{Yb}171Yb spin types.
Abstract We studied the behavior of mixtures of 173Yb (with symmetry up to SU(6)) and 171Yb (up to SU(2)) fermionic isotopes loaded in one-dimensional (1D) optical lattices. To do so, we solved the Schrödinger equation describing different systems using a diffusion Monte Carlo technique. We considered continuous Hamiltonians in which the interactions between atoms of different species (isotopes and/or spins) were modeled by contact potentials with parameters derived from their experimental scattering lengths. This implies that we can find both attractive and repulsive interactions between fermion pairs in the same cluster. The strength of those interactions can be changed by varying the transverse confinement, leading to different cluster behaviors. Only balanced clusters, i.e. with the same number of 173Yb and 171Yb atoms were considered. We found that the standard state for these clusters is a metallic-like one with different populations of 173Yb–171Yb molecule-like pairs in each optical lattice potential well. However, for big enough clusters, insulator-like states are also possible.
Diffusion Monte Carlo calculations on the possibility of having self-bound one-dimensional droplets of SU(6) $\ifmmode\times\else\texttimes\fi{}$ SU(2) ultracold fermionic mixtures are presented. We found that, even though arrangements with attractive interactions with only two spin types are not self-bound, mixtures with at least three kinds of fermions form stable small drops. However, that stabilization decreases for very tight confinements, where a universal behavior is found for Fermi-Fermi and Fermi-Boson clusters including attractive and repulsive interactions.
By means of a diffusion Monte Carlo technique, we study one-dimensional unbalanced mixtures of fermionic ytterbium atoms (173Yb^{173}\mathrm{Yb}173Yb and 171Yb^{171}\mathrm{Yb}171Yb). This means clusters in which the total number of 173Yb^{173}\mathrm{Yb}173Yb particles is different from the sum of all the atoms belonging to the 171Yb^{171}\mathrm{Yb}171Yb 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 171Yb^{171}\mathrm{Yb}171Yb particles with different spins with respect to the number of spin-polarized 173Yb^{173}\mathrm{Yb}173Yb atoms. Clusters in which the number of repulsively interacting unequal-spin 173Yb^{173}\mathrm{Yb}173Yb atoms are in excess with respect to the spin-polarized 171Yb^{171}\mathrm{Yb}171Yb particles have a very narrow stability range.
By using a diffusion Monte Carlo (DMC) technique, we studied the behaviour of a mixture of spin-up and spin-down cold fermionic atoms confined in one-dimensional harmonic potentials. We considered only small balanced clusters (up to eight atoms) or arrangements in which the difference between the population of fermions with different spins is one (with a maximum total number of nine). The atom–atom interactions were modeled by a contact repulsive potential. We focused on the ordering of the confined fermions, finding that the probability of having a pure antiferromagnetic arrangement of atoms decreases strongly with the number of fermions, as to be almost negligible for our largest clusters. Exactly the same can be said of a pure ferromagnetic state.
Abstract The behaviour of fermion clusters with SU(N) symmetry loaded in one-dimensional optical lattices and described by continuous Hamiltonians was studied using a diffusion Monte Carlo (DMC) technique. The state diagrams of SU(6) and SU(2) arrangements with the same number of particles were calculated and found virtually identical. The only difference was the absence of a band insulator in the SU(N) case in the range of optical lattice depths considered (V 0 = 0–12 E R ; E R , recoil energy of the lattice) in the non-interacting limit for N > 2. The appearance of that state was signalled by a noticeable change in the shape of the momentum distributions in going from a metal to a band insulator.
We numerically investigated the collapse of one-dimensional boson–fermion mixtures with fermion–boson attractive interactions. With Monte Carlo simulations, we observed spatial distributions of the particles and the behavior of several physical quantities to find the evidence of the collapse. With strong fermion–boson attractions and weak interboson repulsions, almost all the bosons and a part of the fermions were found to gather in a small space. In this collapse process we identified the role of each microscopic parameter such as boson number density, total number densities of the fermions and the bosons, and the interboson repulsion. We show a phase diagram to locate the collapsed phase in the parameter space of the interactions.