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arXiv:0707.3209 · Physical Review Letters

Commensurability Effects for Fermionic Atoms Trapped in 1D Optical Lattices

Rafael A. Molina, J. Dukelsky, Peter Schmitteckert

Published Aug 24, 2007• 17 citations
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Abstract

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.

DOI
10.1103/physrevlett.99.080404

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Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.
Ground-state properties of fermionic mixtures confined in a one-dimensional optical lattice are studied numerically within the spinless Falicov-Kimball model with a harmonic trap. A number of remarkable results are found. i) At low particle filling the system exhibits phase separation with heavy atoms in the center of the trap and light atoms in the surrounding regions. ii) Insulating phases always coexist with metallic phases. iii) Atomic-density waves are observed in the insulating regions for all particle fillings near the half-filled lattice case. iv) The variance of the local density exhibits universal behavior (independent of the particle filling, the Coulomb interaction and the strength of a confining potential) over the whole region of the local density values.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to an harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.
We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.
We investigate two-component ultracold fermionic atoms with attractive interactions trapped in a two-dimensional optical lattice at zero temperature. By introducing a superfluid trial state with spatially modulated order parameters, we perform the variational Monte Carlo simulations to treat the correlation effects beyond mean-field treatments. It is shown that there appears a strong tendency to the formation of a density wave state in the regions with specific values of local atom density. We then analyze two kinds of perturbations to the superfluid state and show that a coexisting state of superfluid and density wave ordering, a sort of supersolid state, can be stabilized. It is discussed how the trap potential and the resulting spatial modulation of the superfluid state affect the momentum distributions and the noise correlation functions.
We study the ground-state properties of spin-1/2 fermionic atoms confined in a one-dimensional optical superlattice with harmonic confinement by using the density-matrix renormalization group method. For this purpose, we consider an ionic Hubbard model that has superlattice potentials with two-site periodicity. We find that several different types of insulating regimes coexist even if the number of atoms at each site is not an integer, but its average within the unit cell is an integer or half integer. This is contrasted to the coexisting phase of the metallic and Mott-insulating regimes known for the ordinary Hubbard model in an optical lattice. The phase characteristics are elucidated by investigating the profiles of the atom density, the local density (spin) fluctuations, the double occupation probability, and the spin correlations in detail.