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Electric-field-controlled F\"orster resonance energy transfer (FRET) betweenRydberg helium (He) atoms and ground-state ammonia (NH$_3$) molecules has beenstudied at translational temperatures below 100 mK. The experiments wereperformed in an intrabeam collision apparatus with pulsed supersonic beams ofNH$_3$ seeded in He. A range of F\"orster resonances, between triplet Rydbergstates in He with principal quantum numbers of 38, 39 and 40, and the inversionintervals in NH$_3$ were investigated. Resonance widths as low as $100\pm20$MHz were observed for Rydberg-Rydberg transitions with electric dipoletransition moments of 3270 D. These widths result from binary collisions at amean center-of-mass speed of $19.3\pm2.6$ m/s. For transitions in which theinitially prepared Rydberg states were strongly polarized, with large inducedstatic electric dipole moments, van der Waals interactions between thecollision partners increased the resonance widths to $\sim750$ MHz. Frommeasurements of the rate of FRET for the narrowest resonances observed, adensity of NH$_3$ of $(9.4\pm0.3)\times10^{9}$ cm$^{-3}$ in the upperground-state inversion sublevel in the interaction region of the apparatus wasdetermined non-destructively.

physical review. a/physical review, a

Probing van der Waals interactions and detecting polar molecules by  F\"orster resonance energy transfer with Rydberg atoms at temperatures below  100 mK