# Dirac, Rashba and Weyl type spin-orbit couplings: toward experimental realization in ultracold atoms

## TL;DR

This paper proposes experimentally feasible optical Raman lattice schemes to realize various spin-orbit couplings in ultracold atoms, including Dirac, Rashba, and Weyl types, enabling exploration of high-dimensional SO physics and topological phases.

## Contribution

It introduces new optical Raman lattice schemes for realizing multiple types of spin-orbit couplings in ultracold atoms without fine-tuning, enhancing experimental accessibility.

## Key findings

- Long-lived Bose-Einstein condensates with 2D Dirac SO coupling achieved.
- Schemes for 2D Rashba and 3D Weyl SO couplings proposed with current laser technology.
- $^{133}$Cs atoms identified as ideal candidates for realization.

## Abstract

We propose a hierarchy set of minimal optical Raman lattice schemes toward the experimental realization of spin-orbit (SO) couplings of various types for ultracold atoms, including two-dimensional (2D) Dirac type of $C_4$ symmetry, 2D Rashba and 3D Weyl types. These schemes are well accessible with current cold-atom technology, and in particular, a long-lived Bose-Einstein condensation of the 2D Dirac SO coupling has been experimentally proved. The generation of 2D Rashba and 3D Weyl types has an exquisite request that two sources of laser beams have distinct frequencies of factor-two difference. Surprisingly, we find that $^{133}$Cs atoms provide an ideal candidate for the realization. A common and essential feature is the absence of any fine-tuning and phase-locking in the realization, and the resulted SO coupled ultracold atoms have a long lifetime. These schemes essentially improve over the current experimental accessibility and controllability, and open new experimental platforms to study high-dimensional SO physics and novel topological phases with ultracold atoms.