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AIP conference proceedings

Spin Correlation and Superfluidity of Trapped Fermi Atoms on an Optical Lattice

Masahiko Machida, Susumu Yamada, Yoji Ohashi, Hideki Matsumoto

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with repulsive interaction U in the presence of an optical lattice. Applying the exact diagonalization method to a one‐dimensional fermion‐Hubbard model including the trap potential, we find that, when U exceeds a critical value, the binding energy of two Fermi atoms becomes negative indicating that an attractive interaction effectively works. In this case, a “Mott core” appears in the trap center, where each site is occupied by one atom, and a large Cooper‐pair amplitude develops between atoms in the left and right hand sides of this core. In order to clarify the origin of the attractive force, we compute a pseudo spin correlation between neighboring sites given by 〈Si⋅Si+1〉. As a result, we find that a creation of a singlet pair between both sides of the Mott core is strongly coupled with a pseudo‐spin singlet re‐formation leading to an energy gain process.

DOI
10.1063/1.2354607

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Journal of the Physical Society of Japan•Feb 10, 2009•0 citations
We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with repulsive interaction U in the presence of an optical lattice. Applying the exact diagonalization method to a one‐dimensional fermion‐Hubbard model including the trap potential, we find that, when U exceeds a critical value, the binding energy of two Fermi atoms becomes negative indicating that an attractive interaction effectively works. In this case, a “Mott core” appears in the trap center, where each site is occupied by one atom, and a large Cooper‐pair amplitude develops between atoms in the left and right hand sides of this core. In order to clarify the origin of the attractive force, we compute a pseudo spin correlation between neighboring sites given by 〈Si⋅Si+1〉. As a result, we find that a creation of a singlet pair between both sides of the Mott core is strongly coupled with a pseudo‐spin singlet re‐formation leading to an energy gain process.
We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with a repulsive interaction in the presence of an optical lattice. Applying the exact diagonalization method to a one-dimensional Hubbard model including the trap potential, we find that, when the strength of the repulsive interaction exceeds a critical value, the binding energy of two Fermi atoms becomes negative below the half-filling case, indicating that an attractive interaction effectively works between Fermi atoms. In this case, a "Mott insulating core" appears in the center of the trap, where each site is occupied by one atom. The Cooper-pair correlation strongly develops between atoms in the left- and right-hand sides of this core.
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.
We study the limit of large on-site repulsion of the one-dimensional Bose-Hubbard model at low densities, and derive a strong-coupling effective Hamiltonian. By taking the lattice parameter to zero, the Hamiltonian becomes a continuum model of fermions with attractive interactions. The leading corrections to the internal energy of a hard-core-boson (Tonks) gas as well as the (finite temperature) pair correlations of a strongly interacting Bose gas are calculated. We explore the possibility of realizing, in an optical lattice, a Luttinger liquid with stronger density correlations than the Tonks gas. A quantum phase transition to a charge-density-wave Mott insulator is also discussed.
Confinement of atoms by laser technology has opened up a new field of physics. Following the realization of Bose– Einstein condensation (BEC) of bosonic atoms, fermionic atom systems and even boson–fermion mixture systems were successfully trapped and cooled. Application of a periodic potential, so called optical lattice, could also unveil interesting nature of the atoms. One of the interesting phenomena of the atoms on optical lattice is Mott transition. Although there is a long history of the study on bosons or fermions on lattice, coexistence of bosons and fermions on lattice is a rather new topic to study. In particular, we have little knowledge about strongly-correlated bosons and fermions on lattice. In our previous works we performed numerical simulations of Bose–Fermi mixtures to clarify the phase diagram and the effect of the confinement potential. When the total number of bosonic and fermionic atoms per site takes an integer value and interatomic interactions are sufficiently strong, the system would undergo Mott transition where the local atom density is fixed to the integer value. A characteristic of this Mott insulating phase is that a boson and fermion located next to each other can exchange their positions by going through a virtual doubly-occupied state with the atom exchange energy t ’ tbtf=Ubf where tb and tf are the hopping energy of the bosons and fermions respectively and Ubf denotes the on-site interaction between the boson and the fermion. Although there still remain a number of open questions on the Mott state of Bose–Fermi mixtures, the property of superfluid state of the strongly-correlated bosons and fermions has yet to be revealed. In this short note we would like to focus on strongly-correlated Bose–Fermi mixtures at commensurate filling in a three-dimensional periodical potential and see characteristic behaviors, if any, of the superfluid phase close to the phase boundary to the Mott insulating phase. In the following analysis we assume uniformity of the system and thus neglect the possibility of the emergence of so-called supersolid where superfluidity and structural long-range order coexist. For simplicity we ignore all the internal degree of freedom of the atoms and the influence of the trap potential which in fact creates a nonuniform density profile of the bosons and fermions. For the system at commensurate filling on optical lattice, we assume that the interatomic interactions are weak enough to avoid formation of Mott state but strong enough to allow us to expect that there are only few empty or doublyoccupied sites and most sites are singly occupied. Namely we analyze the system that stays in a superfluid phase but lies close to the boundary to the Mott phase. Since a boson and fermion located next to each other can exchange their positions as stated above, the energy of the superfluid state of the mixture system is given mostly by the kinetic energy of the bosons and fermions exchanging their positions. We therefore express the Hamiltonian in the following form, ignoring the kinetic energy of the atoms at the empty sites and the interaction energy at the doubly-occupied sites: