Effective single-band models for strongly interacting fermions in an optical lattice

Abstract

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 $t-J$ model, and the effective superexchange term, $J$, 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 on-site 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.

7 pages, 7 figures; minor typos corrected

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Cited by in corpus (8)

• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Quantum simulation of correlated-hopping models with fermions in optical lattices
• Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
• Lattice Induced Resonances in One Dimensional Bosonic Systems
• Fractional Chern Insulators in Bands with Zero Berry Curvature
• Nagaoka ferromagnetism in doped Hubbard models in optical lattices
• Strongly interacting fermions in an optical lattice
• Spin dynamics dominated by superexchange via virtual molecules