Atomic lattice clocks have spurred numerous ideas for tests of fundamental physics, detection of general relativistic effects, and studies of interacting many-body systems. On the other hand, molecular structure and dynamics offer rich energy scales that are at the heart of new protocols in precision measurement and quantum information science. Here we demonstrate a fundamentally distinct type of lattice clock that is based on vibrations in diatomic molecules, and present coherent Rabi oscillations between weakly and deeply bound molecules that persist for 10's of milliseconds. This control is made possible by a state-insensitive magic lattice trap that weakly couples to molecular vibronic resonances and enhances the coherence time between molecules and light by several orders of magnitude. The achieved quality factor Q = 8 × 10 11 results from 30-Hz narrow resonances for a 25-THz clock transition in Sr2. Our technique of extended coherent manipulation is applicable to long-term storage of quantum information in qubits based on ultracold polar molecules, while the vibrational clock enables precise probes of interatomic forces, tests of Newtonian gravitation at ultrashort range, and model-independent searches for electron-to-proton mass ratio variations.

Processes that break molecular bonds are typically observed with molecules occupying a mixture of quantum states and successfully described with quasiclassical models, while a few studies have explored the distinctly quantum mechanical low-energy regime. Here we use photodissociation of diatomic strontium molecules to demonstrate the crossover from the ultracold, quantum regime where the photofragment angular distributions strongly depend on the kinetic energy, to the energyindependent quasiclassical regime. Using time-of-flight velocity map imaging for photodissociation channels with millikelvin reaction barriers, we explore photofragment energies in the 0.1-300 mK range experimentally and up to 3 K theoretically, and discuss the energy scale at which the crossover occurs. Furthermore, we find that the effects of quantum statistics can unexpectedly persist to high photodissociation energies.

At ultralow energies, atoms and molecules undergo collisions and reactions that are best described in terms of quantum mechanical wave functions. In contrast, at higher energies these processes can be understood quasiclassically. Here, we investigate the crossover from the quantum mechanical to the quasiclassical regime both experimentally and theoretically for photodissociation of ultracold diatomic strontium molecules. This basic reaction is carried out with a full control of quantum states for the molecules and their photofragments. The photofragment angular distributions are imaged, and calculated using a quantum mechanical model as well as the WKB and a semiclassical approximation that are explicitly compared across a range of photofragment energies. The reaction process is shown to converge to its high-energy (axial recoil) limit when the energy exceeds the height of any reaction barriers. This phenomenon is quantitatively investigated for two-channel photodissociation using intuitive parameters for the channel amplitude and phase. While the axial recoil limit is generally found to be well described by a commonly used quasiclassical model, we find that when the photofragments are identical particles, their bosonic or fermionic quantum statistics can cause this model to fail, requiring a quantum mechanical treatment even at high energies.