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New Journal of Physics

One-dimensional SU(N) clusters of fermions in optical lattices

M. C. Gordillo

Published Sep 24, 2019• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/ab4725

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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.
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 different states (metal, Mott insulator, and band insulator) appearing in clusters of fermions confined in one-dimensional optical lattices. To describe these systems, instead of the standard Hubbard Hamiltonian, a continuous model with repulsive contact interactions between unlike-spin particles is used. The corresponding Schr\"odinger equations are solved using a diffusion Monte Carlo algorithm. We consider both balanced (same number of spin-up and spin-down fermions) and unbalanced arrangements with the same number of atoms in the minority component (N=5N\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}5N=5). We find that the structure of the clusters in both the weak- and the strong-coupling limits can be predicted to some extent from the solutions of the noninteracting Schr\"odinger equations describing the same systems, in line with findings in the previous literature.
The behavior of small clusters of one spin-up and two spin-down fermions with unlike-spin repulsive interactions in one-dimensional optical lattices was calculated using a diffusion Monte Carlo technique. We considered also a harmonic potential in the longitudinal direction to make our system resemble the standard experimental setups. When the interparticle repulsion is strong enough, the onset of fermionization is observed irrespective of the optical lattice parameters considered, in line with previous results for pure harmonic confinement. However, fermionization can also be seen even for small interparticle couplings if the optical potential is deep enough. In addition, for certain values of the wavelengths and the potential depths defining the lattice, Mott insulators in the fermionization limit with only three atoms were found.
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.
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.