Rydberg atoms are highly excited atoms that have large sensitivities to external fields, lending these atoms extraordinary characteristics for fundamental high-precision spectroscopy as well as for electromagnetic-field sensing applications. Recent results on high-precision spectroscopy with cold Rydberg atoms in modulated optical lattices are presented. The discussed approach can serve as a platform for fundamental-physics studies, which include a model-insensitive measurement of the Rydberg constant and a search for wave-like dark matter. As an example for the utility of Rydberg atoms in field sensing applications, an experiment is presented in which the linear Stark effect of cold Rydberg atoms is employed to measure electric fields in cold ion clouds, demonstrating that Rydberg laser spectroscopy allows electrode-free, non-invasive plasma diagnostics.
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