Long-lived entanglement of molecules in magic-wavelength optical tweezers

Realising quantum control and entanglement of particles is crucial for advancing both quantum technologies and fundamental science. Significant developments in this domain have been achieved in a variety of systems. In this context, ultracold polar molecules offer new and unique opportunities due to their more complex internal structure associated with vibration and rotation, coupled to the existence of long-range interactions. However, the same properties make molecules highly sensitive to their environment, impacting their coherence and utility in some applications. Here we show that by engineering an exceptionally controlled environment using rotationally-magic optical tweezers, we can achieve long-lived entanglement between pairs of molecules using hertz-scale interactions. We demonstrate the highest reported fidelity to date for a two-molecule Bell state ($0.976^{+0.014}_{-0.016}$) and present the first realisation of a microwave-driven entangling gate between two molecules, preparing the molecules in a decoherence-free subspace. We show that the magic-wavelength trap preserves the entanglement, with no measurable decay over 0.5 s, opening new avenues for quantum-enhanced metrology, ultracold chemistry and the use of rotational states for quantum simulation, quantum computation and as quantum memories. The extension of precise quantum control to complex molecular systems will allow their additional degrees of freedom to be exploited across many domains of quantum science.