Competing Orders in a Dipolar Bose-Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective

Abstract

We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar Bose-Einstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of $D_4$, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of $D_4$. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the d_{x^{2}-y^{2}}-wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with $d_{xy}$- and g-wave symmetries but not enough for them to dominate other competing phases.

18 pages, 9 figures

References in corpus (24)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• A High Phase-Space-Density Gas of Polar Molecules
• Bose-Einstein Condensation of Erbium
• Observation of dipole-dipole interaction in a degenerate quantum gas
• A Mixture of Bose and Fermi Superfluids
• Ultracold dense gas of deeply bound heteronuclear molecules
• Spontaneously modulated spin textures in a dipolar spinor Bose-Einstein condensate
• Quantum degenerate two-species Fermi-Fermi mixture coexisting with a Bose-Einstein condensate
• Mixtures of Bosonic and Fermionic Atoms in Optical Lattices
• Ultracold Heteronuclear Fermi-Fermi Molecules
• Metastable states of a gas of dipolar bosons in a 2D optical lattice
• Realization of a strongly interacting Bose-Fermi mixture from a two-component Fermi gas
• Supersolid Bose-Fermi Mixtures in Optical Lattices
• Feshbach resonances in mixtures of ultracold ${}^6$Li and ${}^{87}$Rb gases
• Engineering Superfluidity in Bose-Fermi Mixtures of Ultracold Atoms
• Competing Orders in two-dimensional Bose-Fermi mixtures
• Supersolidity of cold-atom Bose-Fermi mixtures in optical lattices
• Bose-Fermi mixtures in an optical lattice
• Generalized Dynamical Mean-Field Theory for Bose-Fermi Mixtures in Optical Lattices
• Mean-field phase diagram of the Bose-Fermi Hubbard model
• Pairing and density-wave phases in Boson-Fermion mixtures at fixed filling
• Phases and collective modes of hardcore Bose-Fermi mixture in an optical lattice
• Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field

Cited by in corpus (3)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Unconventional superfluids of fermionic polar molecules in a bilayer system
• Detecting Entrainment in Fermi-Bose Mixtures