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=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.
We present diffusion Monte Carlo calculations on the behavior of a mixture of
173Yb and
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 species and two
171Yb spin types.
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.
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.
We study the momentum distributions and spatial correlations of few harmonically confined SU(
N) fermions using quantum Monte Carlo methods. In our study, we vary the spin degeneracy
N from 2 to 6 and the total number of particles from 6 to 18. Only balanced mixtures, with the same number of atoms per spin type, and repulsive unlike-spin contact interactions are considered. Going from
N=2 to
N=6, with the same occupancy of each spin state, we observe an increase of atom-atom correlations. This effect is particularly significant in the momentum distributions, which show fatter tails at large
k ($k\ensuremath{\sigma}\phantom{\rule{0.16em}{0ex}}>\phantom{\rule{0.16em}{0ex}}5, \ensuremath{\sigma}$ being the oscillator length) when
N grows, in agreement with experimental findings. Those tails also show the expected ${k}^{\ensuremath{-}4}$ decay related to the Tan contact for different values of the spin degeneracy. According to our results, the local spin ordering and the spin-spin correlations are mainly determined by
N via the Pauli exclusion principle, with minor influences from the particle-particle interactions, irrespective of the total number of confined atoms.
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.