## 4 Conclusions  
In conclusion, we have presented the first direct observation of the THz modes emitted by a DFG-QCL frequency comb by multiheterodyne detection with an optically rectified THz comb, referenced to the primary frequency standard, that is a 10-MHz quartz-oscillator disciplined by a Rb-GPS (Global Positioning System) clock (stability of 6 \(\times\) 10\({}^{-13}\) in 1 s and absolute accuracy of 2 \(\times\) 10\({}^{-12}\)). Thanks to our setup, the THz QCL comb modes frequencies could be simultaneously retrieved with a 1 MHz accuracy, confirming that they are actually equally spaced in frequency, at this level of precision. Moreover, by tuning the ratio between the mode spacings of the two combs to an integer value, we observe the HBN collapsing, as expected from a frequency comb.  
Unfortunately, due to the low emitted power-per-mode, only 7% of the total modes could be down-converted, and state-of-the-art techniques such as FACE could not be applied to the THz emission. This could have confirmed the existence of a fixed phase relation among the modes, that is ultimately the true frequency comb signature. However, further improvements in output power can be achieved by the adoption of an optimized device structure with a long-wavelength nonlinear active region [42] and silicon-based THz waveguide [52]. Once the power issues are overcome, not only can the FACE technique confirm phase coherence in the THz emitted modes, but also this technology can fully deploy its promising potential for broadband precision spectroscopy in the THz range, even without cryogenic cooling systems. The latter would pave the way for miniaturized precise metrology diagnostics in the THz range.  
Figure 7: Retrieval of the optically rectified frequency comb (OR-comb) mode number M relative to Equation (1). The frequency of the QCL-comb mode involved in the beating is kept constant by fixing the device driving current and operational temperature. The frequency of the down converted beatnote HBN is acquired and plotted as a function of the optically rectified comb repetition rate (f\({}_{\text{rep}}\)). As a consequence, the order M is extracted from the slope of the data linear regression, by rounding to the nearest integer, i.e., M = 9705. The fit residuals, plotted in red, confirm the 1 MHz uncertainty in the determination of the f\({}_{\text{HBN}}\) frequency.  
**Author Contributions:** [PERSON] supervised the OR comb based characterization experiments, [PERSON] and [PERSON] carried out the measurements and analyzed the data, [PERSON], [PERSON], [PERSON] and [PERSON] discussed the results. [PERSON] fabricated the DFB gratings and performed the buried heterostructure device processing. [PERSON] carried out the QCL growth. [PERSON] designed and characterized devices, and analyzed the data, [PERSON] and [PERSON] discussed the results. [PERSON] and [PERSON] conceived the concept of the experiment and supervised the research. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was founded by MIC/SCOPE #195006001, Qombs Project, EU-H2020-FET Flagship on Quantum Technologies grant no. 820419, the Italian ESFRI Roadmap (Extreme Light Infrastructure-ELI), EC-H2020 Laserlab-Europe grant agreement 871124.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.  
**Acknowledgments:** Authors at Hamamatsu Photonics thank [PERSON] for his helpful support and comments, [PERSON] expresses his thanks to [PERSON] of the Technical University of Munich, and [PERSON] of TransWave Photonics, L.L.C. for helpful discussions.  
**Conflicts of Interest:** The authors declare no conflict of interest.