We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by dynamical mean-field approximation. It is demonstrated that a supersolid state, where an s-wave superfluid coexists with a density-wave state with a checkerboard pattern, is stabilized by attractive onsite interactions on a square lattice. Our new finding here is that a confining potential plays an invaluable role in stabilizing the supersolid state. We establish a rich phase diagram at low temperatures, which clearly shows how an insulator, a density wave and a superfluid compete with each other to produce an interesting domain structure. Our results shed light on the possibility of the supersolid state in fermionic optical lattice systems.

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair potential in the systems with different clusters, we discuss the stability of a supersolid state, where an s-wave superfluid coexists with a density-wave state of checkerboard pattern. It is clarified that a confining potential plays an essential role in stabilizing the supersolid state. The phase diagrams are obtained for several effective particle densities.Comment: 7 pages, 5 figures, Phys. Rev. A in pres

The superfluid-insulator transitions of the fermionic atoms in optical lattices are investigated by the two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of the multiband effects. The quasiparticle weight in the superfluid state decreases significantly, as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model. PACS numbers: 03.75.Lm, 05.30.Fk, 73.43.Nq Since the superfluid of trapped atomic Fermi gases 40 K and 6 Li was observed [1,2,3,4,5,6], intense theoretical and experimental studies have been done for ultracold atomic Fermi gases. In these experiments, magnetic-field Feshbach resonances provide the means for controlling both the strength of the interaction between fermionic atoms and its sign [7]. These tunable interactions enable us to observe the crossover between the BCS superfluid for the weak attractive interaction and the Bose-Einstein condensate (BEC) of bound pairs for the strong attractive interaction. Furthermore, by loading atoms into optical lattices, diverse interaction configurations can be introduced. The combination of these two experimental techniques plays an important role in the study of ultracold fermionic atoms and offers the experimental description of various intriguing quantum many-body phenomena.Recent experiments revealed fascinating aspects of fermionic atoms in three dimensional optical lattices [8,9]. In the ETH experiment, a band insulator in the lowest band was produced, i.e. two atoms in different hyperfine states occupy the lowest state per lattice site [8]. Controlling the interaction, they further observed the partially populated higher bands. In the MIT experiment, a superfluidity of fermionic atom pairs in an optical lattice was observed [9]. By increasing the depth of the lattice potential near the Feshbach resonance, a superfluid-insulator transition was observed. They argued that the insulating state was the Mott insulator. In these experiments, it was argued that the usual singleband Hubbard model was no longer applicable, because the strength of the on-site interaction exceeded the gap between the lowest and the next-lowest bands. For detailed investigations of the experiments, accordingly, the effects of the higher bands have to be taken into account.Stimulated by these experiments, several theoretical studies on the superfluid-insulator transition were carried out [10,11,12]. However, both the correlation effects and the multiband effects have not yet been investigated well enough to discuss the transition from superfluid to Mott insulator. Precise studies including both effects are thus required.In this paper, we investigate the superfluid-insulator transition of interacting fermionic atoms in optical lattices, taking into account the multiband effects. For this purpose, we make use of a dynamical mean-field theory (DMFT) [13]. This method ena...

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We study the two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half-filling the atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while the antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, the quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in respective regions. Systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half-filling. The results are discussed using the effective boson model derived for the strong attractive interaction.

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