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We theoretically propose an idea to reach the $p$-wave superfluid phase in anultracold Fermi gas. The key of our idea is that the pairing symmetry of aFermi superfluid is fully dominated by the symmetry of the superfluid orderparameter, which is essentially given by the product of a pair amplitude and apairing interaction. Noting this, in our proposal, we first prepare a $p$-wavepair amplitude by, not using a $p$-wave interaction, but using the phenomenonthat a $p$-wave pair amplitude is induced in an $s$-wave superfluid Fermi gaswith antisymmetric spin-orbit interaction. In this case, although the system isstill in the $s$-wave superfluid state with the $s$-wave superfluid orderparameter, when one suddenly replaces the $s$-wave interaction by anappropriate $p$-wave one (which is possible in cold Fermi gases by using aFeshbach resonance technique), the product of the $p$-wave interaction and the$p$-wave pair amplitude that has already been prepared in the spin-orbitcoupled $s$-wave superfluid state immediately gives a finite $p$-wavesuperfluid order parameter. Thus, at least just after this manipulation, thesystem is in the $p$-wave superfluid state, being characterized by theartificially produced $p$-wave superfluid parameter. In this paper, to assessour 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 thestrengths of the $s$-wave pairing interaction and the spin-orbit coupling. Wealso discuss the accessibility of this optimal region on the viewpoint of thesuperfluid phase transition temperature. Since the achievement of a $p$-wavesuperfluid Fermi gas is one of the most crucial issues in cold atom physics,our proposal would be useful for this exciting challenge.

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