Proposed method to realize the $p$-wave superfluid state using a $s$-wave superfluid Fermi gas with a synthetic spin-orbit interaction

We theoretically propose an idea to reach the $p$-wave superfluid phase in an ultracold Fermi gas. The key of our idea is that the pairing symmetry of a Fermi superfluid is fully dominated by the symmetry of the superfluid order parameter, which is essentially given by the product of a pair amplitude and a pairing interaction. Noting this, in our proposal, we first prepare a $p$-wave pair amplitude by, not using a $p$-wave interaction, but using the phenomenon that a $p$-wave pair amplitude is induced in an $s$-wave superfluid Fermi gas with antisymmetric spin-orbit interaction. In this case, although the system is still in the $s$-wave superfluid state with the $s$-wave superfluid order parameter, when one suddenly replaces the $s$-wave interaction by an appropriate $p$-wave one (which is possible in cold Fermi gases by using a Feshbach resonance technique), the product of the $p$-wave interaction and the $p$-wave pair amplitude that has already been prepared in the spin-orbit coupled $s$-wave superfluid state immediately gives a finite $p$-wave superfluid order parameter. Thus, at least just after this manipulation, the system is in the $p$-wave superfluid state, being characterized by the artificially produced $p$-wave superfluid parameter. In this paper, to assess our idea, we evaluate the $p$-wave pair amplitude in a spin-orbit coupled $s$-wave superfluid Fermi gas at $T=0$. We determine the region where a large $p$-wave pair amplitude is obtained in the phase diagram with respect to the strengths of the $s$-wave pairing interaction and the spin-orbit coupling. We also discuss the accessibility of this optimal region on the viewpoint of the superfluid phase transition temperature. Since the achievement of a $p$-wave superfluid Fermi gas is one of the most crucial issues in cold atom physics, our proposal would be useful for this exciting challenge.