A Novel Route to Reach a $p$-wave Superfluid Fermi Gas

We theoretically propose an idea to realize a $p$-wave superfluid Fermi gas. To overcome the experimental difficulty that a $p$-wave pairing interaction to form $p$-wave Cooper pairs damages the system before the condensation growth, we first prepare a $p$-wave pair amplitude (${\mathrm{\Phi }}_p$) in a spin-orbit coupled $s$-wave superfluid Fermi gas, without any $p$-wave interaction. Then, by suddenly changing the $s$-wave interaction with a $p$-wave one ($U_p$) by using a Feshbach resonance, we reach the $p$-wave superfluid phase with the $p$-wave order parameter being symbolically written as $\Delta_{p}\sim U_{p}\Phi_{p}$. In this letter, we assess this scenario within the framework of a time-dependent Bogoliubov-de Gennes theory. Our results would contribute to the study toward the realization of unconventional pairing states in an ultracold Fermi gas.