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We theoretically investigate a spin-orbit coupled $s$-wave superfluid Fermigas, to examine the time evolution of the system, after an $s$-wave pairinginteraction is replaced by a $p$-wave one at $t=0$. In our recent paper, weproposed that this manipulation may realize a $p$-wave superfluid Fermi gas,because the $p$-wave pair amplitude that is induced in the $s$-wave superfluidstate by a parity-broken antisymmetric spin-orbit interaction gives anon-vanishing $p$-wave superfluid order parameter, immediately after the$p$-wave interaction is turned on. In this paper, using a time-dependentBogoliubov-de Gennes theory, we assess this idea under various conditions withrespect to the $s$-wave and $p$-wave interaction strengths, as well as thespin-orbit coupling strength. From these, we clarify that the momentumdistribution of Fermi atoms in the initial $s$-wave state ($t<0$) is a key toproduce a large $p$-wave superfluid order parameter. Since the realization of a$p$-wave superfluid state is one of the most exciting and difficult challengesin cold Fermi gas physics, our results may provide a possible way to accomplishthis.

Appropriate conditions to realize a $p$-wave superfluid state starting from a spin-orbit coupled $s$-wave superfluid Fermi gas