Effects of a dilute gas of fermions on the superfluid-insulator phase diagram of the Bose-Hubbard model

Abstract

Building on the work of Fisher et al. (Phys. Rev. B 40, 546 (1989)), we develop a framework for perturbation theory in the Bose-Hubbard model and apply it to calculate the effects of a degenerate gas of spin-polarized fermions interacting by contact interactions with the constituent bosons. For the single-band Bose-Hubbard model, the only non-trivial effect of the fermions is to induce an effective space- and time-dependent density-density interaction among the bosons. Using a path integral formulation, we develop the appropriate theory describing the perturbative effects of this fermion-mediated interaction (fermionic screening) on the generic superfluid-insulator phase diagram. For the single-band Bose-Hubbard model, we find that the net effect of the fermions is to inherently suppress the Mott-insulating lobes and enhance the area occupied by the superfluid phase in the phase diagram. For the more general multi-band Bose-Hubbard model, we find that, in addition to the fermion screening of the boson interactions, the virtual excitations of the bosons to the higher Bloch bands coupled with the contact interactions with the fermions result in an effective increase of the boson on-site repulsion. If this renormalization of the boson on-site potential is dominant over the fermion screening of the boson interactions, the area of the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions, as seen in recent experiments.

16 pages, 5 eps figures; final version to appear in PRB

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Bose-Fermi Mixtures in a Three-dimensional Optical Lattice
• Localization of bosonic atoms by fermionic impurities in a 3d optical lattice
• Mixtures of Bosonic and Fermionic Atoms in Optical Lattices
• Two lectures on color superconductivity
• Role of interactions in 87Rb-40K Bose-Fermi mixtures in a 3d optical lattice
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Supersolid Bose-Fermi Mixtures in Optical Lattices
• Quasiparticle decay rate of Josephson charge qubit oscillations
• Self-Trapping of Bosons and Fermions in Optical Lattices
• Mixture of bosonic and spin-polarized fermionic atoms in an optical lattice
• The one-dimensional Bose-Fermi-Hubbard model in the heavy-fermion limit
• One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons
• Do mixtures of bosonic and fermionic atoms adiabatically heat up in optical lattices?
• Bose-Fermi mixtures in an optical lattice
• Exotic Superconducting Phases of Ultracold Atom Mixtures on Triangular Lattices
• Superfluid-insulator transition in Fermi-Bose mixtures and the orthogonality catastrophe
• Loss of superfluidity by fermions in the boson Hubbard model on an optical lattice
• Boson Hubbard model with weakly coupled Fermions
• Superfluid-Insulator Transition and Fermion Pairing in Bose-Fermi Mixtures

Cited by in corpus (3)

• Effect of interactions on harmonically confined Bose-Fermi mixtures in optical lattices
• Zero-temperature phase diagram of Bose-Fermi gaseous mixtures in optical lattices
• Bose-Fermi solid and its quantum melting in an one-dimensional optical lattice