Pairing between fermions that attract each other, reveal itself to the macroscopic world in the form of superfluidity. Since the discovery of fermionic superfluidity, intense search has been going on to find various unconventional forms of fermion pairing as well as to increase the transition temperature. Here, we show that a two dimensional mixture of single-component fermions and dipolar bosons allows to reach experimentally feasible superfluid transition temperatures for non-standard pairing symmetries. Excitations in these superfluids are anyonic and their statistics depends on the order of their permutations, i.e is non-Abelian. Our results provide for the first time an example of a highly tunable system which exhibits various kind of pairing symmetry and high transition temperature. Additionally, they provide a playground to observe anyonic excitations and their braiding properties.
We develop a strong-coupling theory for the superfluidity of fermion pairing phase in a Bose-Fermi mixture. Dynamical screening, self-energy renormalization, and a pairing gap function are included self-consistently within the adiabatic limit (i.e., the phonon velocity is much smaller than the Fermi velocity). An analytical solution for the transition temperature (T(c)) is derived within reasonable approximations. Using typical parameters of a 40K-87Rb mixture, we find that the calculated T(c) is several times larger than that obtained in the weak coupling theory, and can be up to several percent of the Fermi temperature.
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.
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.