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Simple molecules at ultracold temperatures, particularly when combined with high-resolution optical spectroscopy, open the door to molecular and fundamental science that is hard to access with other physical systems. In this talk, we address unique experiments with diatomic molecules trapped in optical lattices, such as observation of deep subradiance and its use for precision measurements, studies of asymptotic atom-molecule regime, and quantum-state controlled photofragmentation. We also discuss prospects for applying this ‘molecular clock’ to discovering new physics.

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