Thermodynamic properties of two-component fermionic atoms trapped in a two-dimensional optical lattice

We study the finite temperature properties of two-component fermionic atoms trapped in a two-dimensional optical lattice. We apply the self-energy functional approach to the two-dimensional Hubbard model with a harmonic trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott insulating and metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusp-like anomaly at lower temperatures, suggesting a second or higher order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.Comment: 9 pages, 13 figure

Color Superfluid and Trionic State of Attractive Three-Component Lattice Fermionic Atoms at Finite Temperatures

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low temperature region, a second-order transition occurs from a Fermi liquid to a color superfluid (CSF). In the strong attractive region, a first-order transition occurs from a CSF to a trionic state. In the high temperature region, a crossover between a Fermi liquid and a trionic state is observed with increasing the strength of the attractive interaction. The crossover region for fixed temperature is almost independent of filling.Comment: 8 pages, 5 figures, Final version, Mod. Phys. Lett. B 25, 987 (2011

Time-of-flight imaging method to observe signatures of antiferromagnetically ordered states of fermionic atoms in an optical lattice

We propose a simple method to detect the antiferromagnetic (AF) state of fermionic atoms in an optical lattice by combining a time-of-flight (TOF) imaging method and a Feshbach resonance. In this scheme, the nontrivial dynamics of fermionic atoms during the imaging process works as a probe with respect to the breaking of the translational symmetry in the AF state. Precise numerical simulations demonstrate that the characteristic oscillatory dynamics induced by the scattering process that transfers an AF ordering vector appears in TOF images, which can be easily observed experimentally.Comment: 4 pages, 5 figure

Superfluid, staggered state, and Mott insulator of repulsively interacting three-component fermionic atoms in optical lattices

We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of the interactions. As the temperature increases, phase transitions occur from the staggered ordered states to the unordered Mott states. Deviating from half filling, an exotic superfluid state appears close to a regime in which the Mott transition occurs. We explain the origin of these phase transitions and present the finite-temperature phase diagrams.Comment: 24 pages, 16 figure

Superfluid state of repulsively interacting three-component fermionic atoms in optical lattices

We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.Comment: 5 pages, 6 figure