Towards quantum simulation with $^{23}$Na$^{40}$K molecules in optical lattices

We review recent progresses towards simulating quantum many-body physics with polar $^{23}$Na$^{40}$K molecules in optical lattices. First, we extend the coherence time of rotational state by one order of magnitude to about 10 ms in a dilute gas using a spin-decoupled magic trap. We observe density-dependent coherence times, which can be explained by dipolar interactions in the bulk gas. Second, we demonstrate a rotation-dependent dipole trap by utilizing a rotational transition manifold $| X^1 \Sigma^+, v=0, J=0,1\rangle \to | b^3\Pi, v=0, J=0,1,2 \rangle$. The configuration of the trap can be tuned between magic, tune-out, and anti-magic by changing the laser detuning in a few GHz. The photon scattering rate in the trap is negligible thanks to the narrow linewidth of the transition. Finally, we report the progress of preparing high filling $^{23}$Na$^{40}$K molecules in a 3D optical lattice.