Calibration of the THz electric fields using precision physics of the hydrogen molecular ions

Atom-based quantum technologies enable standards for the electromagnetic fields with an important role in science, technology and everyday life. Comparing to previous detection approaches based on antennas, the atom-based measurements improve sensitivity, stability, resolution and reproducibility performances. Based on invariant atomic properties, such measurements are self-calibrated, as they translate electric field strengths into Rabi frequencies that depend on atomic constants. Compact experimental setups were demonstrated in the microwave and up to the sub-THz domain by exploiting the Autler-Townes effect and the electromagnetic induced transparency in Rydberg spectroscopy of alkali atoms. It is not possible to express exactly the relevant alkali atom parameters in function of the SI fundamental constants. On the experimental side, full measurement of a monochromatic electromagnetic wave requires determination not only of its amplitude or power but also of the polarization, the phase and the angle-of-arrival. Development of multi-parameter quantum measurement techniques are required for future quantum sensing applications. Increase in frequency is also needed, as the THz-waves have applications in precision measurements for fundamental physics, free-space communications, remote sensing and medical diagnosis, but the ‘THz gap’ lacks of competitive calibration capabilities.
The hydrogen molecular ions (HMI) are the simplest three-body quantum systems. The frequencies of HMI transitions and their shifts in external fields were calculated accurately by ab-initio quantum molecular theory and precisely measured with Doppler-free spectroscopy of trapped and sympathetically cooled molecular ions. The comparison of precise experimental measurements with accurate ab-initio theory predictions of the frequency shifts induced on HD+ transitions by external fields may be exploited for full electromagnetic field calibration against the values of the fundamental constants and the SI second. Precisely, a THz-wave slightly detuned to the fundamental rotational transition of HD+ may be non-destructively detected using the lighshift induced on the two-photon fundamental vibrational transition. The metrological performances of this approach are subsequently evaluated using the state-of-the-art HMI precision physics. This method enables sensitivity to low THz-wave intensity at the 10^(-8) W/m2 level. A THz-wave with an intensity at the W/m2 level may be calibrated with 10^(-3) fractional uncertainty limited by the accuracy of the ab-initio theory prediction of the lightshift. The static magnetic field in the ion trap may be also calibrated by Zeeman spectroscopy and is exploited further as a directional reference for full characterization of the THz-wave electric field. Six lightshift measurements for suitable magnetic field strengths and orientations in the trap may be converted into the polarization ellipse of the THz electric field, which is described in the ideal laboratory frame with three electric field amplitudes and two phases. Such approach enables determination of the Cartesian components of the electric field of a linearly polarized THz-wave with 1 W/m2 intensity with uncertainties at the mV/m level for the amplitudes and the mrad level for the phases.
This contribution proposes an application of precision physics in quantum technologies that ensures full traceability of the THz electric field measurements by accounting uncertainties in frequency measurements with HD+ ions and their ab-initio theory predictions based on fundamental physical constants.