Triplet pair amplitude in a trapped s-wave superfluid Fermi gas with broken spin rotation symmetry

We investigate the possibility that the broken spatial inversion symmetry caused by a trap potential induces a spin-triplet Cooper pair amplitude in an s-wave superfluid Fermi gas. Based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is actually induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped s-wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a p-wave superfluid Fermi gas by suddenly changing the s-wave pairing interaction to a p-wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into a spin-singlet (and even-parity) state and a spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such an admixture has recently attracted much attention in the field of noncentrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, from the viewpoint of cold Fermi gas physics.