# Spin-exchange-induced exotic superfluids in a Bose-Fermi spinor mixture

## TL;DR

This paper proposes a method to realize spin-orbit coupled Fermi gases and exotic superfluid phases using a Bose-Fermi mixture, where fermions acquire effective spin-orbit coupling via interactions with spin-orbit coupled bosons.

## Contribution

It introduces a novel approach to induce spin-orbit coupling in fermions through boson-fermion interactions, enabling topological superfluids without Raman heating and enhancing observable density stripe phases.

## Key findings

- Fermions gain effective spin-orbit coupling via spin-exchange interactions.
- The presence of fermions enhances the bosonic stripe phase and increases its spatial period.
- The system offers a practical platform for exploring spin-orbit physics and topological phases.

## Abstract

We consider a mixture of spin-1/2 bosons and fermions, where only the bosons are subjected to the spin-orbit coupling induced by Raman beams. The fermions, although not directly coupled to the Raman lasers, acquire an effective spin-orbit coupling through the spin-exchange interaction between the two species. Our calculation shows that this is a promising way of obtaining spin-orbit coupled Fermi gas without Raman-induced heating, where the long-sought topological Fermi superfluids and topological bands can be realized. Conversely, we find that the presence of fermions not only provides a new way to create the supersolid stripe phase of the bosons, but more strikingly it can also greatly increase the spatial period of the bosonic density stripes, and hence makes this phase directly observable in the experiment. This system provides a new and practical platform to explore the physics of spin-orbit coupling, which possesses a dynamic nature through the interaction between the two species.