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 BoseEinstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of D4, 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 D4. 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 dxy-and g-wave symmetries but not enough for them to dominate other competing phases.

QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

“…Studying the dressing of (interacting) fermionic atoms submerged in a superfluid Bose gas [98], the study of the sympathetic cooling technique [99] to cool down spin-polarised fermions which do not interact in the s-wave channel, etc., are only a few of the experimental platforms for the rich physics concealed by Bose-Fermi mixtures (BFM). On the theoretical side, the BFH model is seen as a playground for the understanding of exotic phases of matter [100,101,102,103], such as the coexistence of superfluid and checkerboard order, supersolid states, and the emergence of dressed compound particles. It is also a natural candidate for the search of manifestations of supersymmetry in condensed matter.…”

Detecting Entrainment in Fermi-Bose Mixtures

“…The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase [49][50][51], time-reversal-invariant superfluids with exotic topological properties [52], rotational responses [53] and the dynamics and structure of solitons [54], can be explored by tuning the mass-ratios, particle densities, and interparticle interactions. Interesting physical properties such as, the ground state characteristics of a mixture [55], quasiparticle excitation spectrum [56], general phase diagram [57], phase competition among density wave orderings and superfluid pairings [58], and many-body effects in the mixture [59] have been explored in great detail in the presence of optical lattice potentials, facilitating the interplay between non-linearity and periodicity. Entrainment, in particular, has been investigated theoretically for two- [60][61][62][63] and multi-component [64] Bose-Bose mixture in optical lattices.…”