Sub-Doppler frequency metrology in HD for test of fundamental physics

Weak transitions in the (2,0) overtone band of the HD molecule at $\lambda = 1.38 \, \mu$m were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1) = $217\,105\,181\,895\,(20)$ kHz; R(2) = $219\,042\,856\,621\,(28)$ kHz; R(3) = $220\,704\,304\,951\,(28)$ kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.