  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.
