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arXiv:0805.4261 · Physical Review B

Mott phase in polarized two-component atomic Fermi lattice gas

Masahiko Machida, Masahiko Okumura, S. Yamada, Tetsuo Deguchi, Yoji Ohashi, H. Matsumoto

Published Dec 12, 2008• 10 citations
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Abstract

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 $S=1/2$ antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.

DOI
10.1103/physrevb.78.235117

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We study polarization effects of two-component atomic Fermi gases loaded on three-leg triangular optical lattice by using the density-matrix renormalization-group method. Concentrating on a case in which a Mott phase coexists with metallic ones, we observe plateulike structures in the Mott phase polarization as a function of the input population imbalance. The structures are clearly analogous to the magnetization plateau states studied in the triangular Heisenberg lattice model under the magnetic field. In fact, we find that spin patterns peculiar to the plateau states emerge inside the Mott phase. This result suggests that the Mott phase is an excellent stage in systematically investigating frustrated spin systems.
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.
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We study low-temperature properties of the four-component Fermi gas of neutral atoms in optical lattice for several cases of explicit breaking of the SU(4) pseudospin symmetry in the framework of the Fermi–Hubbard model. For a reduced two-site system, we analyze the energy states and effective magnetic couplings in cases, where four interacting spin flavors in the Hubbard Hamiltonian form the symmetry subgroups of the type “three by one” or “two by two” according to their tunneling and interaction amplitudes, independently, and study behavior of the corresponding effective Heisenberg models in the limit of strong interaction. We also obtain and analyze the spatial density distributions of spin components in a harmonic optical trap for each case of explicit symmetry breaking.