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arXiv:0809.0505 · Physical Review Letters

Metastable Superfluidity of Repulsive Fermionic Atoms in Optical Lattices

Achim Rosch, David Rasch, Benedikt Binz, Matthias Vojta C

Published Dec 29, 2008• 124 citations
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Abstract

In the fermionic Hubbard model, doubly occupied states have an exponentially large lifetime for strong repulsive interactions U. We show that this property can be used to prepare a metastable s-wave superfluid state for fermionic atoms in optical lattices described by a large-U Hubbard model. When an initial band-insulating state is expanded, the doubly occupied sites Bose condense. A mapping to the ferromagnetic Heisenberg model in an external field allows for a reliable solution of the problem. Nearest-neighbor repulsion and pair hopping are important in stabilizing superfluidity.

DOI
10.1103/physrevlett.101.265301

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Journal of the Physical Society of Japan•Feb 10, 2009•0 citations
In the fermionic Hubbard model, doubly occupied states have an exponentially large lifetime for strong repulsive interactions U. We show that this property can be used to prepare a metastable s-wave superfluid state for fermionic atoms in optical lattices described by a large-U Hubbard model. When an initial band-insulating state is expanded, the doubly occupied sites Bose condense. A mapping to the ferromagnetic Heisenberg model in an external field allows for a reliable solution of the problem. Nearest-neighbor repulsion and pair hopping are important in stabilizing superfluidity.
We studied the superfluidity of strongly repulsive fermionic atoms in optical lattices. Atoms are paired through a correlated tunneling mechanism, which induces superfluidity when repulsive nearest-neighbor interactions are included in the Hubbard model. This paired superfluid is a metastable state, which persists for a long time as the pair-broken process is severely suppressed. The mean-field phase diagram and low-energy excitations are investigated in a square lattice system. Intriguingly, spontaneous superflows may appear in the ground state of a triangular optical lattice system due to antiferromagnetic frustration.
We determine the superfluid transition temperatures Tc{T}_{c}Tc​ and the ground states of the attractive Hubbard model and find unusual insulating phases associated with noninteger filling at sufficiently strong pairing attraction $\ensuremath{\mid}U\ensuremath{\mid}$. These states, distinct from the band-and Mott-insulating phases, derive from pair localization; pair hopping at large $\ensuremath{\mid}U\ensuremath{\mid}$ and high densities is impeded by intersite, interpair repulsive interactions. The best way to detect the breakdown of superfluidity is by using fermionic optical lattices, which should reveal these unusual forms of ``bosonic'' order, reflecting ground-state pairing without condensation.
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 investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond ddd-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole ehole(x){e}_{\mathrm{hole}}(x)ehole​(x) has a minimum at doping x=xcx={x}_{c}x=xc​ that signals phase separation between the antiferromagnetic and ddd-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.
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: