Multiband-driven superfluid-insulator transition of fermionic atoms in optical lattices: A dynamical mean-field-theory study

Abstract

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 In these experiments, it was argued that the usual singleband Hubbard model was no longer applicable, because the strength of the on-site interaction exceeded the gap between the lowest and the next-lowest bands.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...

Density-wave and antiferromagnetic states of fermionic atoms in optical lattices

“…6. In the large D region, the band insulator comes into existence [10]. In the small D region, the ADW state and the AF state appear.…”

“…We apply here the two-site DMFT method [19], which allows us to study the Mott transitions of orbitally degenerate lattice fermions qualitatively [20,21]. To study the superfluid of lattice fermions, we extend this method to the case when the superfluid order exists [10].…”

“…Recently, we have investigated the superfluid-insulator transition of fermionic atoms in optical lattices beyond the conventional meanfield approximation, taking two-band effects into account [10]. It was shown that the Mott insulating state appears for the adequately strong interaction region at half-filling.…”

“…A Mott insulating state [5,6,7,8,9,10,11] and/or ordered states [12,13,14,15] for fermionic atoms in two-or three-dimensional optical lattices have been investigated by various theoretical methods. Recently, we have investigated the superfluid-insulator transition of fermionic atoms in optical lattices beyond the conventional meanfield approximation, taking two-band effects into account [10].…”

Transition from band insulator to Bose-Einstein-condensate superfluid and Mott state of cold Fermi gases with multiband effects in optical lattices

“…Since this condition is hardly realized in electron systems and is not fully studied, unexpected mechanisms or phenomena as well as internal degrees of freedom of molecular bosons may play important roles. Some theoretical works suggested possible insulator-superfluid transitions caused by the attractive interactions [15,16,17,18,19]. So far, however, little is known on the character of the transition and on properties of phases around the transition point with thermal effects.…”