Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

New Journal of Physics

Metal and insulator states of SU(6) × SU(2) clusters of fermions in one-dimensional optical lattices

M. C. Gordillo

Published May 20, 2021• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/ac0387

Related papers

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

M. C. Gordillo

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.

Physical Review A•Aug 31, 2020•4 citations

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

M. C. Gordillo

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.

New Journal of Physics•Sep 24, 2019•2 citations

States of one-dimensional fermion clusters with repulsive interactions in optical lattices

M. C. Gordillo

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 ($N\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}5$). 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.

Physical Review A•Sep 25, 2017•3 citations

Fermionization and Mott-insulator formation in fermion trimers loaded in one-dimensional optical lattices

M. C. Gordillo, Feliciano De Soto

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.

Physical Review A•Jul 12, 2017•6 citations

Paramagnetism in few-fermion clusters with repulsive interactions

M. C. Gordillo

Abstract We describe the possible states of four-fermion clusters loaded in one-dimensional optical lattices with an additional harmonic confinement when the interactions between particles of different spin are contact-like. We have found that, depending on the depth of the potential well, the wavelength of the laser, and the strength of the repulsive interactions, we can have ground states that have unpaired spins (paramagnetic), all the spins paired (diamagnetic) or a degenerate mixture of different configurations. In this last case, the cluster could be either a metal or a Mott insulator. The characteristics of the ground state can be inferred to some extent from the solutions of non-interacting Schrödinger equations for the same arrangements.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 29, 2018•4 citations

Unbalanced droplets of one-dimensional mixtures of fermions

M. C. Gordillo

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.

arXiv:2410.01605•Physical Review A•Feb 18, 2025•0 citations
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 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.
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 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.
Abstract We describe the possible states of four-fermion clusters loaded in one-dimensional optical lattices with an additional harmonic confinement when the interactions between particles of different spin are contact-like. We have found that, depending on the depth of the potential well, the wavelength of the laser, and the strength of the repulsive interactions, we can have ground states that have unpaired spins (paramagnetic), all the spins paired (diamagnetic) or a degenerate mixture of different configurations. In this last case, the cluster could be either a metal or a Mott insulator. The characteristics of the ground state can be inferred to some extent from the solutions of non-interacting Schrödinger equations for the same arrangements.
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.