Non-destructive cavity readout of molecules for precision measurements

We propose a non-destructive method to measure the population of molecules in a selected rotational-hyperfine state by coupling them to a high-finesse optical cavity. In contrast to traditional techniques, our approach enables fast (less than 1 ms) repeated measurements with reduced heating and losses, and with precision below the standard quantum limit. The method is particularly advantageous for radioactive molecules, systems of high interest for symmetry violation searches, for which production and sample size are limited, and repeated interrogation is essential for improved sensitivity.