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Journal of Physics Conference Series

Single-particle excitation spectrum in 1D ultracold fermionic optical lattices

Atsushi Yamamoto, Susumu Yamada, Masahiko Machida

Published Dec 17, 2012• 0 citations
Publisher

Abstract

We investigate the properties of fermions trapped in a one-dimensional (1D) optical lattice by using the density-matrix renormalization (DMRG) group method. Owing to a harmonic confinement potential inherent in real experiments, system becomes inhomogeneous structure. Under certain conditions for weak-repulsive interaction, we find that the single-particle excitation spectrum structure changes to band branching and discrete bound-state states as increasing the trap strength. Additionally, we consider the case of strong-repulsive interacting regimes which local density profile show coexist with central Mott-plateau phase with surrounded by metallic regions. As increasing the trap strength, we find the breakdown of 1D Tomonaga-Luttinger (TL) liquid which is alternative to an effective doping into the Mott phase. We will present the various kinds of striking spectra, show the comparison of repulsive interaction case with attractive interaction one.

DOI
10.1088/1742-6596/400/1/012082

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We investigate the properties of fermions trapped in a one-dimensional (1D) optical lattice by using the density-matrix renormalization (DMRG) group method. Owing to a harmonic confinement potential inherent in real experiments, system becomes inhomogeneous structure. Under certain conditions for weak-repulsive interaction, we find that the single-particle excitation spectrum structure changes to band branching and discrete bound-state states as increasing the trap strength. Additionally, we consider the case of strong-repulsive interacting regimes which local density profile show coexist with central Mott-plateau phase with surrounded by metallic regions. As increasing the trap strength, we find the breakdown of 1D Tomonaga-Luttinger (TL) liquid which is alternative to an effective doping into the Mott phase. We will present the various kinds of striking spectra, show the comparison of repulsive interaction case with attractive interaction one.
We examine spectral properties on one-dimensional (1D) trapped ultracold Fermi atoms loaded on optical lattices by using the dynamical density-matrix renormalization group (DDMRG) method. We find that spectra are very rich due to the interplay of free or repulsive interaction and the harmonic-trap potential. One of the rich examples is that a 1D Tomonaga-Luttinger (TL) liquid spectrum emerges beneath multiple bound-state flat levels in the Mott-plateau phase and the TL spectrum gradually disappears with a partial breakdown of the central Mott plateau by increasing the trap strength. A more striking example is the growth of a distinct low-energy broadened band from the bound-state flat levels together with the breakdown. It demonstrates a carrier doping effect into the Mott phase in optical lattice systems.
We investigate the ground-state properties of fermions trapped in a one-dimensional double-well optical lattice by means of the density-matrix renormalization group method. A weak harmonic confinement potential inherent in real experiments, which makes the system inhomogeneous, is also considered. Under certain conditions for interactions, we find that two kinds of insulating regions coexist at half-filling and three-quarters filling due to the double-well structure and the system inhomogeneity. We further study the dynamical properties of the system by employing the adaptive time-dependent density-matrix renormalization group method. When the double-well lattice is suddenly changed into a normal single-well lattice, the two insulating regions gradually disappear under time evolution, which is accompanied by oscillating behavior of the local density characteristic of many-body fermionic systems.
Recent experiments have made it possible to spatially control local two-body interactions between ultracold atoms in inhomogeneous optical lattices. Motivated by this experimental progress, here we study theoretically one-dimensional trapped fermionic optical lattices with spatially modulated on-site interactions. The density matrix renormalization group method is used to examine the ground state phase diagram of a harmonically trapped Hubbard model with spatially alternating on-site repulsive interactions, U 1 and U 2 . With varying the strength of the harmonic trapping potential, we find a pair correlated metallic state in the ground state phase diagram, which can be stable only when U 1 ≠ U 2 . We discuss the properties of this possibly new state by examining various static physical quantities.
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.
Using the time-dependent density-matrix renormalization-group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.
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.