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arXiv:1401.0241 · Physical Review A

Quantum phases in degenerate- p -orbital attractive one-dimensional fermionic optical lattices

Keita Kobayashi, Yukihiro Ota, Masahiko Okumura, Susumu Yamada, Masahiko Machida

Published Feb 18, 2014• 9 citations
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Abstract

We examine quantum phases emerging from the double degeneracy of $p$-orbital bands in attractive atomic Fermi gases loaded on a one-dimensional (1D) optical lattice. Our numerical simulations via the density-matrix renormalization group predict the emergence of a state with a charge excitation gap, namely the Haldane insulator phase. A mapping onto an effective spin-1 model reveals its physical origin. Moreover, we show that population imbalance leads to richer diversity of the quantum phases, including a phase-separated polarized state. Finally, we study the effects of the harmonic trap potential in this 1D chain.

DOI
10.1103/physreva.89.023625

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We examine quantum phases emerging from the double degeneracy of ppp-orbital bands in attractive atomic Fermi gases loaded on a one-dimensional (1D) optical lattice. Our numerical simulations via the density-matrix renormalization group predict the emergence of a state with a charge excitation gap, namely the Haldane insulator phase. A mapping onto an effective spin-1 model reveals its physical origin. Moreover, we show that population imbalance leads to richer diversity of the quantum phases, including a phase-separated polarized state. Finally, we study the effects of the harmonic trap potential in this 1D chain.
Emergence of ηηη-pairing ground-state in population-imbalanced attractive Fermi-gases filling ppp orbitals on 1-D optical lattice
We explore the ground states in population-imbalanced attractive 1-D fermionic optical lattice filling ppp orbitals over the lowest sss one by using the density-matrix-renormalization-group (DMRG) method. The DMRG calculations find the occurrence of spatially non-uniform off-diagonal long-range order. In contrast to Fulde-Ferrel Larkin-Ovchinikov pair as observed in the single-band Hubbard model. The spatial oscillation period of the pair correlation function is widely fixed to be πππ irrespective of the mismatch between spin-split Fermi surfaces. The ground-state πππ order corresponds to ηηη-pair condensate predicted by Yang [Phys. Rev. Lett. \textbf{63}, 2144 (1989)]. Taking account of the effects of harmonic traps, we confirm that the ηηη-pair state distinctly emerges at the center of the trap potential surrounded by perfectly-polarized states even in the trapped cases.
We propose a method to create a nontrivial Haldane phase in an atomic two-component Fermi gas loaded on a one-dimensional optical lattice with trap potential. The Haldane phase is naturally formed on a p-band Mott core in a wide range of the strong on-site repulsive interaction. The present proposal is composed of two steps, one of which is theoretical derivation of an effective 1D S=1 interacting-chain model from the original tight-binding Hamiltonian handling the two p orbitals, and the other of which is a numerical demonstration employing the density-matrix renormalization group for the formation of the Haldane phase on a p-band Mott core and its associated features in the original tight-binding model with the harmonic trap potential.
We study a multi-orbital Fermi gas loaded on a one-dimensional optical lattice with harmonic trap potential. We show that this multi-orbital gas contains various quantum phases, i.e., (i) the ferromagnetic phase in large on–site interaction and (ii) the Haldane phase at half filling. Furthermore, our density-matrix renormalization-group simulations lead to systematic studies about the ground state, varying on–site interaction, spin imbalance, and total particle number, under spatial inhomogeneity originating from the trap potential. This trap potential produces a rich phase structure. In a metallic region, the phase-separated ferromagnetism appears, whereas in a central Mott core the Haldane phase is found. One of the remarkable features is that the ferromagnetic metal phase behaves as the edge state of the Haldane phase when these two phases coexist.
We investigate effects of optical lattice potential in one- and two-dimensional two-component trapped Fermi gases with population imbalances. Using the exact diagonalization and the density matrix renormalization group methods complementarily, we calculate the atom-density profile from the ground state many-body wave function as a function of attractive interaction strength for various population imbalances. The numerical results reveal that although a phase separation between the superfluid core and the shell cloud of excess atoms occurs as observed in experiments without the optical lattice, the population imbalance generally remains in the core region in contrast to the nonlattice cases. The essence of the numerical results in a strong attractive regime can be explained by an effective model composed of Cooper pairs and excess major fermions.
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.
We investigate effects of pseudospin population imbalance on Mott phases in one-dimensional trapped two-component atomic Fermi gases loaded on optical lattices based on the repulsive Hubbard model in harmonic traps. By using the density-matrix renormalization-group method, we numerically calculate density profiles of each component and clarify the pseudospin magnetism. Consequently, we find that all the features from weakly imbalance to fully polarized cases are well described by S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.