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arXiv:cond-mat/0603299 · Physical Review A

Fermions in optical lattices near a Feshbach resonance: From band insulator to Mott insulator

A. F. Ho

Published Jun 14, 2006• 17 citations
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Abstract

We study a model of an equal mixture of two species of fermions in a deep optical lattice at a filling of two fermions per site. At weak interspecies interaction, the system is a band insulator. When the interspecies interaction is tuned via a Feshbach resonance to be larger than an energy related to the energy separation of the first and second Bloch bands, atoms populate equally the two Bloch bands. With weak tunneling between sites of the optical lattice, the system becomes a Mott insulator with the low-energy effective Hamiltonian of a spin-1 Heisenberg antiferromagnet, because of a Hund's-rule-like coupling between the two bands. We discuss experimental signatures of these two types of insulators.

DOI
10.1103/physreva.73.061601

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We study a model of an equal mixture of two species of fermions in a deep optical lattice at a filling of two fermions per site. At weak interspecies interaction, the system is a band insulator. When the interspecies interaction is tuned via a Feshbach resonance to be larger than an energy related to the energy separation of the first and second Bloch bands, atoms populate equally the two Bloch bands. With weak tunneling between sites of the optical lattice, the system becomes a Mott insulator with the low-energy effective Hamiltonian of a spin-1 Heisenberg antiferromagnet, because of a Hund's-rule-like coupling between the two bands. We discuss experimental signatures of these two types of insulators.
We theoretically investigate, using non-perturbative strong correlation techniques, Mott insulating phases and magnetic ordering of two-component fermions in a two-dimensional double-well optical lattice. At filling of two fermions per site, there are two types of Mott insulators, one of which is characterized by spin-1 antiferromagnetism below the Neel temperature. The super-exchange interaction in this system is induced by the interplay between the inter-band interaction and the spin degree of freedom. A great advantage of the double-well optical lattice is that the magnetic quantum phase diagram and the Neel temperature can be easily controlled by tuning the orbital energy splitting of the two-level system. Particularly, the Neel temperature can be one order of magnitude larger than that in standard optical lattices, facilitating the experimental search for magnetic ordering in optical lattice systems.
We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.
We theoretically investigate, using nonperturbative strong correlation techniques, Mott-insulating phases and magnetic ordering of two-component fermions in a two-dimensional double-well optical lattice. At filling of two fermions per site, there are two types of Mott insulators, one of which is characterized by spin-1 antiferromagnetism below the N\'eel temperature. The superexchange interaction in this system is induced by the interplay between the interband interaction and the spin degree of freedom. A great advantage of the double-well optical lattice is that the magnetic quantum phase diagram and the N\'eel temperature can be easily controlled by tuning the orbital energy splitting of the two-level system. Particularly, the N\'eel temperature can be one order of magnitude larger than that in standard optical lattices, facilitating the experimental search for magnetic ordering in optical lattice systems.
To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double-well potential. From the spectrum, we determine the range of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective ttt-JJJ model, and the effective superexchange term, JJJ, can be smoothly tuned through zero on either side of unitarity. Right at and around unitarity, an effective one-band general Hubbard model is appropriate, with a finite and small onsite energy, due to a lattice-induced anharmonic coupling between atoms at the scattering threshold and a weakly bound Feshbach molecule in an excited center-of-mass state.
We investigate the ground-state properties of an equal mixture of two species of bosons in its Mott-insulator phase at a filling factor of two per site. We identify one type of spin triplet-singlet transition through the competition of the ground state. When the on-site interaction is weak (U<Uc)(U<{U}_{c})(U<Uc​) the two particles prefer to stay in the lowest band and with weak tunneling between neighboring sites the system is mapped into an effective spin-1 ferromagnetic exchange Hamiltonian. When the interaction is tuned by a Feshbach resonance to be large enough (U>Uc)(U>{U}_{c})(U>Uc​), the higher band will be populated. Due to the orbital coupling term ${S}^{+}{S}^{\ensuremath{-}}$ in the Hamiltonian, the two atoms in different orbits on a site would form an on-site singlet. For a non-SU(2)-symmetric model, easy-axis or easy-plane ferromagnetic spin exchange models may be realized, corresponding to phase separation or counterflow superfluidity, respectively.
Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion UUU, the model is shown to reproduce the ttt-JJJ Hamiltonian, in which the JJJ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate ggg: explicitly, J=4g2/UJ=4{g}^{2}/UJ=4g2/U. At half-filling, ggg drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0g=0g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=tg=tg=t). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of ggg.