We examine a two-dimensional mixture of single-component fermions and dipolar bosons. We calculate the self-enregies of the fermions in the normal state and the Cooper-pair channel by including first-order vertex correction to derive a modified Eliashberg equation. We predict the appearance of superfluids with various nonstandard pairing symmetries at experimentally feasible transition temperatures within the strong-coupling limit of the Eliashberg equation. Excitations in these superfluids are anyonic and follow non-Abelian statistics.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with
s-,
p-, and
d-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
The recent experimental progress in realizing Bose-Fermi mixtures and dipolar quantum gases has created the exciting possibility of creating dipolar Bose-Fermi mixtures with intriguing and unique properties. In a dipolar condensate, the dipole-dipole interaction represents a control knob inaccessible to nondipolar Bosons. Thus, mixing dipolar bosons with fermions may open up new possibilities for creating superfluids with unconventional pairings. We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in a three-dimensional setting in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We develop a procedure which allows us to determine the parameters such as densities and scattering lengths that are required to achieve optimal critical temperature before the system starts to phase separate. We perform a systematic investigation, finding that a superfluid with a critical temperature, that is orders of magnitude higher than achievable in nondipolar mixtures, can be realized in dipolar mixtures at experimentally accessible densities and scattering lengths before the system phase separates.
Ultracold atom experiments offer the unique opportunity to study mixing of different types of superfluid states. Our interest is in superfluid mixtures comprising of particles with different statistics---Bose and Fermi. Such scenarios occur naturally, for example, in dense quantum chromodynamics (QCD) matter. Interestingly, cold atomic experiments are performed in traps with finite spatial extent, thus critically destabilizing the occurrence of various homogeneous phases. Critical to this analysis is the understanding that the trapped system can undergo phase separation, resulting in a unique situation where phase transition in either species (bosons or fermions) can overlap with the phase separation between possible phases. In the present work, we illustrate how this intriguing interplay manifests in an interacting two-species atomic mixture---one bosonic and another fermionic with two spin components---within a realistic trap configuration. We further show that such interplay of transitions can render the nature of the ground state to be highly sensitive to the experimental parameters and the dimensionality of the system.
A finite-temperature (
T>0) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions
ρB and
ρF, respectively, on a two-dimensional square lattice with composite hopping
t is presented. The composite hopping swaps the locations of a fermion and a boson that occupy nearest-neighbor sites of the lattice. The superfluid order parameter
ψ, the femion hopping amplitude
ϕ, the chemical potential
μ, the free energy minimum
F~ and entropy
S are calculated in the limit
ρB+ρF=1 within a mean-field approximation, and lead to a phase diagram in the
ρF−T plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped
T(ρF), and insulating normal liquid and insulating normal gas phases outside the dome. These phases are separated by coupled discontinuous transitions as indicated by jumps in
ψ and
ϕ. The maximum critical transition temperature
Tc is observed very close to
ρF=1/2. While
F~(T) is continuous with a derivative discontinuity at
T=Tc(ρF) for
01/2 (zeroth-order transition), where the entropy becomes negative for a range of temperatures below
Tc. The ratio of
Tc to Fermi band width agrees remarkably with the ratio of
Tc/
TF (where
TF is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-
Tc cuprates, iron-based and hydride superconductors, that exhibit experimental values of
Tc spread over nine orders of magnitude from
∼200nK to
∼260K.
Unconventional superconductivity and superfluidity are among the most exciting and fascinating quantum phenomena in condensed-matter physics. Usually such states are characterized by nontrivial spin or spatial symmetry of the pairing order parameter, such as ``spin triplet'' or ``
p wave.'' However, besides spin and spatial dependence the order parameter may have unconventional frequency dependence which is also permitted by Fermi-Dirac statistics. Odd-frequency fermionic pairing is an exciting paradigm when discussing exotic superfluidity or superconductivity and is yet to be realized in experiments. In this paper we propose a symmetry-based method of controlling frequency dependence of the pairing order parameter via manipulating the inversion symmetry of the system. First, a toy model is introduced to illustrate that frequency dependence of the order parameter can be achieved through our proposed approach. Second, by taking advantage of recent rapid developments in producing spin-orbit-coupled dispersions in ultracold gases, we propose a Bose-Fermi mixture to realize such frequency-dependent superfluid. The key idea is introducing the frequency-dependent attraction between fermions mediated by Bogoliubov phonons with asymmetric dispersion. Our proposal should pave an alternative way for exploring frequency-dependent superfluids with cold atoms.