Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at $\lambda =1.38\mu \mathrm{m}$ 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 [$R(1)=217105181895(20)\mathrm{kHz}$; $R(2)=219042856621(28)\mathrm{kHz}$; $R(3)=220704304951(28)\mathrm{kHz}$] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

Figure 1

Experimental setup. The spectroscopy laser (ECDL) is sent through a modulator (EOM) to impose both $f_{\mathrm{PDH}}$ and $f_{\mathrm{FSR}}$ modulations. $f_{\mathrm{PDH}}$ is used to stabilize the laser (carrier) frequency to the optical cavity (also the HD absorption cell) and $f_{\mathrm{FSR}}$ to generate sideband frequencies that are resonant to adjacent cavity modes. The spectroscopy laser is locked to a Cs atomic clock via an optical frequency comb laser for long-term stabilization. Additional cavity-length dither modulation $f_{\mathrm{dith}}$ is applied for lock-in detection of the HD saturated absorption signals.

Figure 2

Recordings of the HD (2,0) $R(1)$ line for three different pressure conditions averaging 5 scans for 2.0 Pa, 7 scans for 1.0 Pa, and 4 scans for 0.5 Pa. The solid (red) lines are fits using a line shape function based on a derivative of dispersion [23] while allowing for a baseline slope. The curves have been shifted in the vertical direction for clarity. In the upper panel a stick spectrum of the hyperfine structure of this transition is plotted, where the 0-value represents the center-of-gravity.

Figure 3

The saturation spectra of the $R(2)$ and $R(3)$ transitions of the HD (2,0) overtone band at 1 Pa pressure. [$R(2)$: 12-scan average; $R(3)$: 5-scan average]

Figure 4

A pressure-dependent frequency shift (a) and broadening (b) of the $R(1)$ transition in the 0.5 to 5 Pa pressure range. Note that for the broadening, the apparent width is plotted, measured via $1f$-modulation of the NICE-OHMS signal (see text).