Quantum Forces from Dark Matter and Where to Find Them

We observe that sub-GeV dark matter (DM) induces Casimir-Polder forces between nucleons that can be accessed by experiments from nuclear to molecular scales. We calculate the nucleon-nucleon potentials arising in the DM effective theory and note that their main features are fixed by dimensional analysis and the optical theorem. Molecular spectroscopy and neutron scattering turn out be DM search experiments and are found to be complementary to nucleon-based DM direct detection. Existing data set limits on DM with mass up to similar to 3-50 MeV and with effective interaction up to the O(10-100) MeV scale, constraining a region typically difficult to reach for other experiments.