Frequency-Comb-Assisted Terahertz Quantum Cascade Laser Spectroscopy

We report a metrological-grade THz spectroscopy based on the combination of a THz frequency-comb synthesizer (FCS) and a THz quantum cascade laser (QCL). The QCL, emitting at 2.5 THz, is phase locked to the free-space THz FCS, and its frequency is swept across a methanol transition by tuning the comb-repetition rate, which is ultimately disciplined by the Cs primary frequency standard. The absolute frequency scale provides an uncertainty of a few parts in ${10}^{-11}$ on the laser frequency and ${10}^{-9}$ on the line-center determination, ranking this technique among the most precise ever developed in the THz range.

Popular Summary

Quantum cascade lasers (QCLs)—a class of semiconductor lasers based on quantum-well structures—are compact and versatile sources of long-wavelength radiation, representing a major breakthrough in the generation of terahertz (THz) frequencies. Recent studies have shown that their emission has a very high spectral purity (i.e., a narrow intrinsic linewidth), suggesting their use in schemes for high-precision metrology, in particular, for the characterization of low-energy excitations such as the rotational states of molecules, which require THz probing. Here, we report the first metrological-grade application of a QCL, used in combination with a frequency comb—the Nobel-prize-winning metrology tool that has been successful in the visible and infrared range but has only recently been extended to the THz regime. The method led to the measurement of the frequency of the rotational transition of a gas molecule (methanol) with unprecedented accuracy.

The scheme uses a THz frequency comb (a set of thousands of discrete and closely spaced frequencies, generated in a nonlinear crystal by a short-pulse infrared laser) to phase lock the QCL frequency, which can be tuned by controlling the comb repetition rate. The latter is ultimately linked to a primary frequency standard (a cesium atomic clock), providing an absolute frequency reference. The resulting QCL emission linewidth is stable and narrow and can be controllably swept across the rotational absorption lines of methanol to determine their absolute positions. The scheme allows us to measure the frequency of the methanol transition with an uncertainty of $4\times {10}^{-9}$, surpassing the precision of previous measurements by over 1 order of magnitude. This first demonstration may pave the way to a broad range of applications, including novel THz-based astronomy, high-precision trace-gas sensing, cold-molecule physics, and molecular-based THz clocks.

Figure 1

The scheme of the experimental setup is shown, with the diagram describing how the traceability of the primary Cs frequency standard is transferred to the THz QCL-based spectroscopy via the stabilization of the repetition rate ($f_{\text{rep}}$) of the pump laser and the THz FCS. The mechanism for tuning the QCL frequency (${\nu }_{\mathrm{QCL}}$) is also sketched: The beat-note frequency ($f_b$) is kept constant by the phase-lock loop, while the tuning of $f_{\text{rep}}$ produces a proportional shift of the THz comb tooth, and thus of the QCL absolute frequency. The lock-in acquisition of the absorption signal requires the beam intensity to be mechanically modulated by a chopper. HEB–hot-electron bolometer; PID–proportional-intergal-derivative controller.

Figure 2

Spectroscopic signal, recorded by tuning the repetition rate of the Ti:sapphire pump laser. Experimental conditions (gas pressure and temperature) are also reported.

Figure 3

The procedure for the determination of $N$ selects a group of a few tens of lines (within a 10-GHz-wide window—light yellow region) where one may look for the detected line. This line is the only one (blue arrow) whose listed frequency can be retrieved, at the sub-MHz level, by Eq. (1) with the experimental $f_{\text{rep}}$ and $f_b$ values and an integer value of $N$ (see the Supplemental Material [24]). The presence of the pair provides a further confirmation. It is worth noting that a preliminary measurement of the QCL frequency, provided by a FTIR spectrometer (dashed green curve), actually excludes the right transitions.

Figure 4

(a) Experimental absorption profile (blue dots) and Voigt function fit (red line) with residuals (red dots, bottom panel), for the most intense of the two lines investigated. The flat residuals confirm that the adopted fitting function [Voigt profile with linear background; see Eq. (4)] well reproduces the experimental line shape. Gas pressure and temperature during the acquisition are also reported. (b) Dependence of the center-line frequency on gas pressure (black dots), with the corresponding linear fit (red line). The intercept and the slope values of the fit give the absolute frequency (${\nu }_{c0}$) and the pressure shift of the considered line.

Figure 5

The absolute frequency of the same transition has been measured by two other techniques: FTIR spectroscopy and microwave spectroscopy. These results (grey and blue, respectively) are compared with ours (red) and with the most recent prediction of a molecular model (green). In particular, the table summarizes the three consistent results zoomed on the right, evidencing the tenfold improvement of the measurement uncertainty provided by our system.