Cavity-enhanced molecular hydrogen spectroscopy for precision metrology in a deep cryogenic regime

High-finesse cavity-enhanced spectrometers are essential instruments for both fundamental and applied science. Shifting the system’s operating temperature from room temperature to the deep-cryogenic regime offers significant benefits for spectral measurements, such as suppressing Doppler broadening, enhancing peak absorption, narrowing the Boltzmann distribution of rotational states, and freezing out unwanted molecular species.

We report the first cavity-enhanced spectrometer designed to operate fully in the deep cryogenic regime, reaching temperatures as low as 4 K [1]. In our system, the entire optical cavity together with the mirrors and the cavity-length actuator - is cooled uniformly alongside the gas sample, ensuring that the sample remains in thermodynamic equilibrium [2].

We apply the apparatus to Doppler-limited spectroscopy of the S(0) (1–0) rovibrational transition in molecular hydrogen, which enables previously inaccessible molecular-physics measurements, including: precise tests of molecular quantum electrodynamics (QED); an optical realization of primary SI standards for temperature, concentration, and pressure in the deep cryogenic regime; measurement of the H2 phase diagram; and determination of the ortho–para spin-isomer conversion rate.

The S(0) (1–0) transition frequency is measured with a 16 kHz uncertainty and agrees with the latest theory to within 88 kHz, given a 380 kHz uncertainty in the theoretical prediction. This level of agreement tests molecular quantum theory at the 10th significant digit and, to the best of our knowledge, provides the most precise validation of QED in a four-body system to date [3].

[1] Stankiewicz et al., arXiv:2502.12703 (accepted to Nature Physics).

[2] Słowiński et al., Rev. Sci. Instrum. 93, 115003 (2022).

[3] K. Pachucki, J. Komasa, J. Chem. Theory Comput. 2025, 21, 12664−12673.