P-wave superfluid in a quasi-two-dimensional dipolar Bose-Fermi quantum gas mixture*

The $p$-wave ($p_{x} + i p_{y})$ superfluid has attracted significant attention in recent years mainly because its vortex core supports a Majorana fermion which, due to its non-Abelian statistics, can be explored for implementing topological quantum computation (TQC). Mixing in bosons may lead to $p$-wave pairing in a Fermi gas. In a dipolar condensate, the dipole-dipole interaction represents a control knob inaccessible to nondipolar Bosons. Thus, mixing dipolar bosons with fermions opens up new possibilities. We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in a quasi-two-dimensional trap setting. We take the Hartree-Fock-Bogoliubov mean-field approach and develop a theory for studying the stability of the mixture and estimating the critical temperature of the $p$-wave superfluid. We use this theory to identify the experimentally accessible parameter space in which the mixture is stable against phase separation and the $p$-wave superfluid pairing can be resonantly enhanced. An enhanced $p$-wave superfluid order parameter can make the fault tolerant TQC less susceptible to thermal fluctuations. This work aims to stimulate experimental activity in creating dipolar Bose-Fermi mixtures.