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

TL;DR

This paper explores how broken spatial inversion and spin rotation symmetries in a trapped s-wave superfluid Fermi gas can induce a spin-triplet pairing component, with implications for creating p-wave superfluids and understanding non-centrosymmetric superconductivity.

Contribution

It demonstrates, through symmetry analysis and numerical confirmation, that spin-triplet pair amplitudes can be induced in s-wave superfluids under certain symmetry-breaking conditions, suggesting new ways to realize p-wave superfluidity.

Findings

Triplet pair amplitude is induced in trapped s-wave superfluids with broken spin rotation symmetry.

The phenomenon is present in spin-imbalanced s-wave superfluids.

Potential to create p-wave superfluids by changing pairing interactions via Feshbach resonance.

Abstract

We investigate the possibility that the broken spatial inversion symmetry by a trap potential induces a spin-triplet Cooper-pair amplitude in an $s$-wave superfluid Fermi gas. Being 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 really 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 the spin-singlet (and even-parity) state and the 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 admixture has recently attracted much attention in the field of non-centrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, on the viewpoint of cold Fermi gas physics.