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arXiv:cond-mat/0606697 · Physical Review A

Fermionic atoms trapped in a one-dimensional optical superlattice with harmonic confinement

Takanori Yamashita, Norio Kawakami, Makoto Yamashita

Published Dec 22, 2006• 16 citations
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Abstract

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.

DOI
10.1103/physreva.74.063624

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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.
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 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.
We study the ground-state properties of spin-1 bosonic atoms trapped in a one-dimensional optical lattice with harmonic confinement. We have developed a highly efficient numerical method based on the Gutzwiller approximation to clarify the inhomogeneous magnetic phases induced by the harmonic confining potential. A quantum phase transition from a superfluid to a Mott insulator is examined for the respective cases with antiferromagnetic and ferromagnetic interactions. It is shown that the profile of local spins over the lattice sites changes as a function of the interaction strength forming the characteristic structures, which closely correlates with the average number of atoms at the sites. For antiferromagnetic cases, we find that there is a crossover from a superfluid polar condensate to Mott-insulator domains consisting of either a spin-singlet pair or a single spin at each site.
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.
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.
We study the time-dependent dynamical properties of two-component ultracold fermions in a one-dimensional optical superlattice by applying the adaptive time-dependent density matrix renormalization group to a repulsive Hubbard model with an alternating superlattice potential. We clarify how the time evolution of local quantities occurs when the superlattice potential is suddenly changed to a normal one. For a Mott-type insulating state at quarter filling, the time evolution exhibits a profile similar to that expected for bosonic atoms, where correlation effects are less important. On the other hand, for a band-type insulating state at half filling, the strong repulsive interaction induces an unusual pairing of fermions, resulting in some striking properties in time evolution, such as a paired fermion co-tunneling process and the suppression of local spin moments. We further address the effect of a confining potential, which causes spatial confinement of the paired fermions.