# 2D spin-orbit coupling for ultracold atoms in optical lattices

## TL;DR

This paper proposes a versatile method to realize tunable 2D spin-orbit coupling in ultracold atoms using microwave driving and lattice shaking, enabling the simulation of topological insulators with potential for exploring exotic quantum states.

## Contribution

The authors introduce a novel scheme combining microwave driving and lattice shaking to achieve controllable 2D SOC in ultracold atoms with inversion symmetry, including independent tuning of Rashba and Dresselhaus couplings.

## Key findings

- Achieved time-reversal invariant 2D SOC in ultracold atoms.
- Demonstrated independent tuning of Rashba and Dresselhaus SOC strengths.
- Showed potential for realizing topological insulators in cold atom systems.

## Abstract

Spin-orbit coupling (SOC) is at the heart of many exotic band-structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of time-reversal invariant 2D SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators in the presence of SOC, which is closely related to the Kane-Mele model.