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Physical Review A

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

M. C. Gordillo, Feliciano De Soto

Published Jul 12, 2017• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.96.013614

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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 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.
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.
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 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.
We investigate the phase separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of the density-matrix renormalization method. The phase separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between intercomponent fermions. We find the existence of a critical repulsive interaction strength above which the phase separation evolves. By increasing the trap imbalance, the composite phase of the Mott-insulating core is changed into one of the ferromagnetic insulating core, which is incompressible and originates from the Pauli exclusion principle.
Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a nontrivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, which allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.