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

## TL;DR

This paper explores how to induce a $p$-wave superfluid state from an $s$-wave superfluid Fermi gas with spin-orbit coupling by analyzing the system's time evolution after interaction switching, identifying key conditions for success.

## Contribution

It demonstrates, through time-dependent Bogoliubov-de Gennes theory, that initial momentum distribution is crucial for realizing a $p$-wave superfluid from an $s$-wave state with spin-orbit coupling.

## Key findings

- Initial momentum distribution influences $p$-wave order parameter magnitude.
- Spin-orbit coupling and interaction strengths affect the $p$-wave superfluid realization.
- The approach offers a potential pathway to achieve $p$-wave superfluidity in cold Fermi gases.

## Abstract

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