We numerically study the problem of two fermions in a three-dimensional optical lattice interacting via a zero-range Feshbach resonance and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low-energy, low-density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width and can be adapted to multichannel situations or higher-ℓ pairing. In strong contrast to usual Hubbard physics, we find that pair hopping is significantly altered by strong interactions and the presence of the lattice, and the lattice induces multiple molecular bound states.We numerically study the problem of two fermions in a three-dimensional optical lattice interacting via a zero-range Feshbach resonance and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low-energy, low-density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width and can be adapted to multichannel situations or higher-ℓ pairing. In strong contrast to usual Hubbard physics, we find that pair hopping is significantly altered by strong interactions and the presence of the lattice, and the lattice induces multiple molecular bound states.

arXiv:1109.1510Physical Review LettersJul 31, 201215 citations

Orbital order of spinless fermions near an optical Feshbach resonance

Philipp Hauke, Erhai Zhao, Krittika Goyal +3 more

We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the $p$ -band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with ``axial orbital order'' in which ${p}_{z}$ and ${p}_{x}+i{p}_{y}$ (or ${p}_{x}\ensuremath{-}i{p}_{y}$) orbitals alternate.We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the $p$-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with ``axial orbital order'' in which ${p}_{z}$ and ${p}_{x}+i{p}_{y}$ (or ${p}_{x}\ensuremath{-}i{p}_{y}$) orbitals alternate.

arXiv:1103.5964Physical Review ANov 21, 201113 citations

Interacting Fermions in Optical Lattices

Tilman Esslinger

Bulletin of the American Physical SocietyMay 19, 20050 citations

Resonant scattering and microscopic model of spinless Fermi gases in one-dimensional optical lattices

Xiaoling Cui

We study the effective Bloch-wave scattering of a spinless Fermi gas in one-dimensional (1D) optical lattices. By tuning the odd-wave scattering length, we find multiple resonances of Bloch waves scattering at the bottom (and the top) of the lowest band, beyond which an attractive (and a repulsive) two-body bound state starts to emerge. These resonances exhibit comparable widths in the deep lattice limit, and the finite interaction range plays an essential role in determining their locations. Based on exact two-body solutions, we construct an effective microscopic model for the low-energy scattering of fermions. The model can reproduce not only the scattering amplitudes of Bloch waves at the lowest-band bottom or top, but also the attractive or repulsive bound states within a reasonably large energy range below or above the band. These results lay the foundation for quantum simulating topological states in cold Fermi gases confined in 1D optical lattices.We study the effective Bloch-wave scattering of a spinless Fermi gas in one-dimensional (1D) optical lattices. By tuning the odd-wave scattering length, we find multiple resonances of Bloch waves scattering at the bottom (and the top) of the lowest band, beyond which an attractive (and a repulsive) two-body bound state starts to emerge. These resonances exhibit comparable widths in the deep lattice limit, and the finite interaction range plays an essential role in determining their locations. Based on exact two-body solutions, we construct an effective microscopic model for the low-energy scattering of fermions. The model can reproduce not only the scattering amplitudes of Bloch waves at the lowest-band bottom or top, but also the attractive or repulsive bound states within a reasonably large energy range below or above the band. These results lay the foundation for quantum simulating topological states in cold Fermi gases confined in 1D optical lattices.

arXiv:1612.06487Physical Review AApr 7, 20174 citations

Strongly interacting fermions in optical lattices: from few to many particles

Michael L. Wall, Lincoln D. Carr

Bulletin of the American Physical SocietyApr 13, 20130 citations

We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the

p

-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with ``axial orbital order'' in which

{p}_{z}

and

{p}_{x}+i{p}_{y}

(or ${p}_{x}\ensuremath{-}i{p}_{y}$) orbitals alternate.