## 3 THz Multi-Heterodyne Detection  
A more accurate characterization of the spectral emission of the DFG-QCL has been performed at the CNR-INO laboratories in Italy, by mounting it on the cold finger of a liquid Helium cryostat. In order to perform the measurements at the same device operational temperature as the ones reported in the previous paragraph, we measured the resistance of the DFG-QCL device, which is temperature dependent. In fact, due to the different cryostat configurations, the temperature sensors distance from the device can be very different, leading to inconsistent temperature measurements. In the experiments, the QCL device has been driven by means of an ultra-low-noise current driver (ppqSense, QubeCL-P05) at 580 mA. Following the current-voltage curve of the QCL device in Figure 2, this corresponds, at 78 K, to a resistance of about 23.3 \(\Omega\). Therefore, we changed the operational temperature of the device to obtain, at I = 580 mA, an applied voltage of 13.5 V, and therefore the same QCL resistance of 23.3 \(\Omega\). On the QCL mount, a bias-tee (Marki Microwave, BT-0024 SMG) is connected so as to retrieve the radio-frequency (RF) beatings among the different modes emitted, named hereafter intermodal beatnotes (IBNs). These radio-frequency IBNs are acquired by a spectrum analyzer (Rohde-Schwarz, FSW 26.5 GHz). A frequency-comb operation of the FP mid-infrared QCL device requires the presence of a single IBN frequency (\(\rm f_{\rm IBN}\)). For the selected driving current (\(\rm I_{\rm QCL}\) = 580 mA) and device resistance (\(\rm R_{\rm QCL}\) = 23.3 \(\Omega\)), we notice the presence of a single IBN, as reported in Figure 3 (\(\rm f_{\rm IBN}\) = 15.18 GHz) with different spans and resolution bandwidths. Yet, the information retrieved by the intermodal beatnote is not sufficient to confirm a comb-like emission from the FP mid-infrared laser QCL, and, as a consequence, whether the DFG device is emitting a frequency comb in the THz range. To these purposes, we implemented a multi-heterodyne detection setup, detecting the THz  
Figure 2: Current–voltage and light–current characteristics of the mid-infrared pumps at 78 K and THz DFG at various temperatures, for the device operated in continuous-wave (CW) mode. beating of the QCL-comb with a well-known reference frequency comb emitting in the THz range. The THz spectral emission of the DFG-QCL comb is characterized in continuous-wave (CW) mode according to a standard multi-heterodyne detection procedure described in [30,31], with the experimental setup sketched in Figure 4. The reference comb is obtained through optical-rectification (OR) of an amplified mode-locked Erbium-doped fiber fs-laser (Menlo Systems, model FC1500) locked against a primary frequency standard, whose emission is focused in a single-mode Lithium Niobate waveguide. The resulting THz frequency comb, hereafter referred to as OR-comb, presents several advantages: It is very stable (6 Hz stability), it is offset-free, and it has a repetition rate frep continuously tunable from 248 to 252 MHz. This OR-comb radiation is mixed with the QCL emission on a Hot Electron Bolometer (HEB-Scontel RS0.3-3T1), realizing multi-heterodyne detection, and retrieving the down-converted beating RF-signal between the OR- and the QCL-combs, consisting of the beating of each optical mode effectively emitted by the QCL with each OR-comb mode. Figure 4: Experimental setup used for the characterization of the DFG QCL-comb. The beams of the optically rectified comb (OR-comb) and QCL-comb are superimposed by means of a beam splitter (BS) and then mixed on a fast detector (HEB: Hot-electron bolometer). The HEB signal is acquired on a spectrum analyzer (Tektronics RSA5106A), and the intermodal beatnote (IBN) is acquired on a second spectrum analyzer (Rohde Schwarz FSW 26.5 GHz). The OR-comb and both spectrum analyzers are frequency-referenced to the primary frequency standard. BP filter: Band-pass filter.