Seconds-scale coherence on nuclear spin transitions of ultracold polar molecules in 3D optical lattices

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.