We extend our recent work [Y. Endo et al., Phys. Rev. A 92, 023610 (2015)] for a parity-mixing effect in a model of two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at $T=0$, we point out that an odd-parity $p\text{-wave}$ Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s\text{-wave}$ superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the $s\text{-wave}$ pairing interaction to an appropriate $p\text{-wave}$ one by using a Feshbach technique in this case, a nonvanishing $p\text{-wave}$ superfluid order parameter is immediately obtained, which is given by the product of the $p\text{-wave}$ interaction and the $p\text{-wave}$ pair amplitude that has already been induced in the spin-imbalanced $s\text{-wave}$ superfluid Fermi gas. Thus, by definition, the system is in the $p\text{-wave}$ superfluid state, at least just after this manipulation. Since the achievement of a $p\text{-wave}$ superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond the LDA.

• Received 24 August 2016

DOI:https://doi.org/10.1103/PhysRevA.94.043632