Quantum Simulation of the Hubbard Model: The Attractive Route
arXiv:0812.4422 · doi:10.1103/PhysRevA.79.033620
Abstract
We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.
11 pages, 5 figs. New version as accepted in PRA. We have clarified the models we are discussing in various places, and expanded on the critical number estimate to include both K40 and Li6 in section V. Also added references
References in corpus (19)
- Many-Body Physics with Ultracold Gases
- Using photoemission spectroscopy to probe a strongly interacting Fermi gas
- Spatial quantum noise interferometry in expanding ultracold atom clouds
- Imaging the Mott Insulator Shells using Atomic Clock Shifts
- Observation of Vortex Pinning in Bose-Einstein Condensates
- Formation of spatial shell structures in the superfluid to Mott insulator transition
- Pairing states of a polarized Fermi gas trapped in a one-dimensional optical lattice
- Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy
- Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in one-dimensional optical lattices
- Density-Matrix Renormalization Group Study of Trapped Imbalanced Fermi Condensates
- The FFLO state in the one-dimensional attractive Hubbard model and its fingerprint in the spatial noise correlations
- Intrinsic Heating and Cooling in Adiabatic Processes for Bosons in Optical Lattices
- Interaction-Induced Adiabatic Cooling for Antiferromagnetism in Optical Lattices
- Cold Attractive Spin Polarized Fermi Lattice Gases and the Doped Positive U Hubbard Model
- Competing superfluid and density-wave ground-states of fermionic mixtures with mass imbalance in optical lattices
- Polarized superfluidity in the attractive Hubbard model with population imbalance
- Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model
- Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling
- Fermions in optical lattices near a Feshbach resonance: from band insulator to Mott insulator