Floquet engineering ultracold polar molecules to simulate topological insulators

We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on so-called Hopf insulator, which represents three-dimensional state matter existing outside conventional tenfold way and crystalline-symmetry-based classifications insulators. Its topology is protected by linking number invariant, necessitates long-range spin-orbit-coupled hoppings its realization. While these ingredients have so far precluded realization in solid-state systems other architectures, an accompanying Letter [T. Schuster et al., Phys. Rev. Lett. 127, 015301 (2021)], predict that can arise naturally from dipolar interaction. Here, investigate specific molecule architecture, where effective ``spin'' formed sublattice degrees freedom. introduce two techniques allow one to optimize with large band gaps, should also be readily applicable exotic structures. First, describe use Floquet engineering control range functional form and, second, demonstrate molecular AC polarizabilities (under circularly polarized light) used precisely tune resonance condition between different rotational states. To verify this latter technique amenable current-generation experiments, calculate, first principles, polarizability ${\ensuremath{\sigma}}^{+}$ light $^{40}\mathrm{K}^{87}\mathrm{Rb}$. Finally, show experiments are capable detecting unconventional insulator varying termination lattice at edges, gives rise three distinct classes edge mode spectra.