  Ultracold polar molecules (UPMs) are emerging as a novel and powerful
platform for fundamental applications in quantum science. Here, we report
characterization of the coherence between nuclear spin levels of ultracold
ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a
nearly photon scattering limited trapping lifetime of 9(1) seconds. After
identifying and compensating the main sources of decoherence, we achieve a
maximum nuclear spin coherence time of $T_2^* = 3.3(6)$~s with two-photon
Ramsey spectroscopy. Furthermore, based on the understanding of the main factor
limiting the coherence of the two-photon Rabi transition, we obtain a Rabi
lineshape with linewidth below 0.8 Hz. The simultaneous realization of long
lifetime and coherence time, and ultra-high spectroscopic resolution in our
system unveils the great potentials of UPMs in quantum simulation, computation,
and metrology.
