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arXiv:0809.4114 · Physical Review A

Spatially modulated superfluid states in fermionic optical ladder systems with repulsive interactions

Yusuke Fujihara, Akihisa Koga, Norio Kawakami

Published Jan 14, 2009• 10 citations
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Abstract

We investigate two-component ultracold fermionic atoms with repulsive interactions trapped in an optical lattice with ladder structure. By applying the Bogoliubov--de Gennes equations to an effective $t\text{\ensuremath{-}}J$ model in the strong correlation limit, we discuss how the spatially modulated spin-singlet pairs with $d$-wave-like symmetry are formed in the systems with trapping potentials. Furthermore, a close examination of the condensation energy as well as the local average of potential, kinetic, and exchange energies by means of the variational Monte Carlo method elucidates that local particle correlations enhance the stability of the superfluid state via a substantial energy gain due to singlet pairing in the high particle density region.

DOI
10.1103/physreva.79.013610

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We investigate two-component ultracold fermionic atoms with repulsive interactions trapped in an optical lattice with ladder structure. By applying the Bogoliubov--de Gennes equations to an effective t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model in the strong correlation limit, we discuss how the spatially modulated spin-singlet pairs with ddd-wave-like symmetry are formed in the systems with trapping potentials. Furthermore, a close examination of the condensation energy as well as the local average of potential, kinetic, and exchange energies by means of the variational Monte Carlo method elucidates that local particle correlations enhance the stability of the superfluid state via a substantial energy gain due to singlet pairing in the high particle density region.
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.
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 explore in this paper a harmonically trapped asymmetric fermionic superfluid in a two-dimensional optical lattice with pairing interactions between the neighboring sites, by self-consistently solving Bogliubov--de Gennes equations. We find the superfluid generally phase separates into a ddd-wave pairing component and an extended sss-wave pairing one, mixed with the unpaired normal fermions. For sufficient large number asymmetries, the ground state is found to be a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state without fourfold rotational symmetry. Both the ddd-wave and sss-wave order parameters show spatially varying novel patterns with nodal points or nodal lines. These features are expected to be checked by the experiments on the repulsive ultracold fermionic atoms.
We investigate the Bose-Einstein condensation (BEC, superfluidity) of particle-hole pairs in ultracold fermionic atoms with repulsive interactions and arbitrary polarization, which are trapped within optical lattices. In the strongly repulsive limit, the dynamics of particle-hole pairs can be described by a hard-core Bose-Hubbard model. The insulator-superfluid and charge-density-wave- (CDW) superfluid phase transitions can be induced by decreasing and increasing the potential depths with controlling the trapping laser intensity, respectively. The parameter and polarization dependence of the critical temperatures for the ordered states (BEC and/or CDW) are discussed simultaneously.
We consider a strongly repulsive fermionic gas in a two-dimensional optical lattice confined by a harmonic trapping potential. To address the strongly repulsive regime, we consider the $t\ensuremath{-}J$ Hamiltonian. The presence of the harmonic trapping potential enables the stabilization of coexisting and competing phases. In particular, at low temperatures, this allows the realization of a ddd-wave superfluid region surrounded by purely (gapless) normal edges. Solving the Bogoliubov--de Gennes equations and comparing them with the local density approximation, we show that the proximity to the Mott insulator is revealed by a downturn of the Fermi liquid order parameter at the center of the trap where the ddd-wave gap has a maximum. The density profile evolves linearly with distance.