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arXiv:2410.01605 · Physical Review A

Unbalanced droplets of one-dimensional mixtures of fermions

M. C. Gordillo

Published Feb 18, 2025• 0 citations
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Abstract

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.

DOI
10.1103/physreva.111.023321

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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.
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.
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 $\ensuremath{\delta}$ 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 173Yb^{173}\mathrm{Yb}173Yb species and two 171Yb^{171}\mathrm{Yb}171Yb spin types.
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 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.
We study the stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean-field energy can lead to a formation of Bose-Fermi liquid droplets – self-bound systems in three-dimensional space. The stability analysis of the homogeneous case is supported by numerical simulations of finite systems by explicit inclusion of surface effects. We discuss the experimental feasibility of formation of quantum droplets and indicate the main obstacle – inelastic three-body collisions.