Lamb-dip-locked quantum cascade laser for comb-referenced IR absolute frequency measurements

The frequency of a DFB quantum cascade laser (QCL) emitting at 4.3 μm has been long-term stabilized to the Lamb-dip center of a CO 2 ro-vibrational transition by means of first-derivative locking to the saturated absorption signal. Thanks to the non-linear sum-frequency generation (SFG) process with a fiber-amplified Nd:YAG laser, the QCL mid-infrared (IR) radiation has been linked to an optical frequency-comb synthesizer (OFCS) and its absolute frequency counted with a kHz-level precision and an overall uncertainty of 75 kHz. © 2008 Optical Society of America OCIS codes: (140.5965) Semiconductor lasers, quantum cascade; (300.6460) Spectroscopy, saturation; (300.6390) Spectroscopy, molecular; (140.3425) Laser stabilization; (120.3930) Metrological instrumentation; (190.7220) Upconversion References and links 1. D. Mazzotti, G. Giusfredi, P. Cancio and P. De Natale, “High-sensitivity spectroscopy of CO2 around 4.25 μm with difference-frequency radiation,” Opt. Lasers Eng. 37, 143–158 (2002) 2. D. Mazzotti, S. Borri, P. Cancio, G. Giusfredi and P. De Natale, “Low-power Lamb-dip spectroscopy of very weak CO2 transitions near 4.25 μm,” Opt. Lett. 27, 1256–1258 (2002) 3. T. Udem, J. Reichert, R. Holzwarth and T. W. Hänsch, “Absolute Optical Frequency Measurement of the Cesium D1 Line with a Mode-Locked Laser,” Phys. Rev. Lett. 82, 3568–3571 (1999) 4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635– 639 (2000) 5. S. M. Foreman, D. J. Jones and J. Ye, “Flexible and rapidly configurable femtosecond pulse generation in the mid-IR,” Opt. Lett. 28, 370–372 (2003) 6. D. Mazzotti, P. Cancio, G. Giusfredi, P. De Natale and M. Prevedelli, “Frequency-comb-based absolute frequency measurements in the mid-infrared with a difference-frequency spectrometer,” Opt. Lett. 30, 997–999 (2005) 7. P. Maddaloni, P. Malara, G. Gagliardi and P. De Natale, “Two-tone frequency modulation spectroscopy for ambient-air trace gas detection using a portable difference-frequency source around 3 μm,” Appl. Phys. B 85, 219–222 (2006) (C) 2008 OSA 21 July 2008 / Vol. 16, No. 15 / OPTICS EXPRESS 11637 #95282 $15.00 USD Received 21 Apr 2008; revised 12 Jun 2008; accepted 20 Jun 2008; published 18 Jul 2008 8. L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang and Z. B. Gong, “Widely phase-matched tunable difference-frequency generation in periodically poled LiNbO3 crystal,” Opt. Commun. 281, 1686–1692 (2008) 9. L. E. Myers, R. C. Eckardt, M. M. Fejer and R. L. Byer, “Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNbO3,” Opt. Lett. 21, 591–593 (1996) 10. S. Blaser, D. A. Yarekha, L. Hvozdara, Y. Bonetti, A. Muller, M. Giovannini and J. Faist, “Room-temperature, continuous-wave, single-mode quantum cascade lasers at λ 5.4 μm,” Appl. Phys. Lett. 86, 041109 (2005) 11. L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, M. Loncar, M. Troccoli, and F. Capasso, “High-power quantum cascade lasers grown by low pressure metal organic vapor-phase epitaxy operating in continuous wave above 400 K,” Appl. Phys. Lett. 88, 201115 (2006) 12. X. J. Wang, J. Y. Fan, T. Tanbun-Ek and F.–S. Choa, “Low threshold quantum cascade lasers of room temperature continuous-wave operation grown by metal-organic chemical-vapor deposition,” Appl. Phys. Lett. 90, 211103 (2007) 13. S. Blaser, A. Bächle, S. Jochum, L. Hvozdara, G. Vandeputte, S. Brunner, S. Hansmann, A. Muller and J. Faist, “Low-consumption (below 2 W) continuous-wave single-mode quantum cascade lasers grown by metal-organic vapour-phase epitaxy,” Electron. Lett. 43, 1201–1202 (2007) 14. A. Mohan, A. Wittmann, A. Hugi, S. Blaser, M. Giovannini and J. Faist, “Room-temperature continuous-wave operation of an external-cavity quantum cascade laser,” Opt. Lett. 32, 2792–2794 (2007) 15. R. M. Williams, J. F. Kelly, J. S. Hartman, S. W. Sharpe, M. S. Taubman, J. L. Hall, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “Kilohertz linewidth from frequency-stabilized mid-infrared quantum cascade lasers,” Opt. Lett. 24, 1844–1846 (1999) 16. M. S. Taubman, T. L. Myers, B. D. Cannon, R. M. Williams, F. Capasso, C. Gmachl, D. L. Sivco and A. Y. Cho, “Frequency stabilization of quantum cascade lasers by use of optical cavities,” Opt. Lett. 27, 2164–2166 (2002) 17. M. S. Taubman, T. L. Myers, B. D. Cannon and R. M. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta, Part A 60, 34573468 (2004) 18. F. Bielsa, A. Douillet, T. Valenzuela, J. Karr, and L. Hilico, “Narrow-line phase-locked quantum cascade laser in the 9.2 μm range,” Opt. Lett. 32, 1641–1643 (2007) 19. Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini and J. Faist, “Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy,” Appl. Phys. B 82, 149–154 (2006) 20. A. Castrillo, G. Casa and L. Gianfrani, “Oxygen isotope ratio measurements in CO2 by means of a continuouswave quantum cascade laser at 4.3 μm,” Opt. Lett. 32, 3047–3049 (2007) 21. J. T. Remillard, D. Uy, W. H. Weber, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco J. N. Baillargeon and A. Y. Cho, “Sub-Doppler resolution limited Lamb-dip spectroscopy of NO with a quantum cascade distributed feedback laser,” Opt. Express 7, 243–248 (2000) 22. A. Castrillo, E. De Tommasi, L. Gianfrani, L. Sirigu and J. Faist, “Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 μm by means of a distributed feedback quantum cascade laser,” Opt. Lett. 31, 3040–3042 (2006) 23. S. Borri, S. Bartalini, P. De Natale, M. Inguscio, C. Gmachl, F. Capasso, D. L. Sivco and A. Y. Cho, “Frequency modulation spectroscopy by means of quantum cascade lasers,” Appl. Phys. B 85, 223–229 (2006) 24. S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, P. De Natale, S. Borri, I. Galli, T. Leveque and L. Gianfrani, “Frequency-comb-referenced quantum cascade laser at 4.4 μm,” Opt. Lett. 32, 988–990 (2007) 25. The HITRAN database is available at http://cfa-www.harvard.edu/HITRAN 26. V. S. Letokhov, Saturation spectroscopy, in High-Resolution Laser Spectroscopy, K. Shimoda, ed. (Springer, 1976), pp. 96–171 27. T. L. Myers, R. M. Williams, M. S. Taubman, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon and A. Y. Cho “Free-running frequency stability of mid-infrared quantum cascade lasers,” Opt. Lett. 27, 170–172 (2002) 28. H. R. Telle, B. Lipphardt and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002) 29. P. Rabinowitz, R. Keller and J. T. Latourrette, “Frequency stabilization of CO2 lasers with respect to SF6 and CO2 line centers,” in 24th Annual Symposium on Frequency Control,, pp. 275–278, (1970)


Introduction
The most recent trace-gas sensing and frequency metrology applications are increasingly looking toward the mid-IR spectral region, also known as the molecular "fingerprint" region, pushed by the presence of the fundamental ro-vibrational transitions of many simple molecules like CO 2 and CH 4 that are particularly relevant for atmospheric implications (greenhouse effect, pollution monitoring).
Difference-frequency generation (DFG) of tunable light has proven to be a suitable technique for mid-IR trace-gas detection [1], high-resolution spectroscopy [2] and, after the introduction of OFCSs [3,4], precise absolute frequency measurements [5,6].Depending on the visible or near-IR sources used, even assembled in quite compact designs [7], this non-linear process can provide narrow-linewidth and widely-tunable radiation [8].However, DFG-based spectrometers are limited to the mW power range [7] by relatively low conversion efficiencies and have an upper wavelength cut-off imposed by the transparency range of the non-linear material used (about 5 μm for LiNbO 3 ) [9].The recent availability of high-power single-mode QCLs has extended the high-sensitivity and high-precision spectroscopic applications to the mid-IR spectral region, ranging from 3.5 up to 100 μm wavelength.In the last decade the features of these innovative sources have been deeply studied and gradually improved: the working temperature has been raised up to 300 K or even more [10,11], while the threshold current has been sensibly reduced [12,13].Moreover, QCLs have been assembled in external-cavity configurations [14] and have been frequency stabilized by electronic servo-locking [15,16,17] and phase-locking techniques [18].Applications of QCLs for both sensitive trace-gas detection [19,20] and high-resolution sub-Doppler spectroscopy [21,22] have been recently demonstrated.
In the last years, the high versatility of these sources has allowed us to perform both sensitive detection on N 2 O and CH 4 by frequency-modulation spectroscopy [23] and Doppler-limited comb-assisted absolute frequency measurements of CO 2 transitions [24].These experiments pointed out the benefits coming from a frequency stabilization of the QCL: in particular, a higher precision in frequency measurements can be achieved by locking the laser to a narrow reference and averaging the counts over long timescales.
In this paper we report on a long-term frequency stabilization of a 4.3 μm emitting QCL to the Lamb dip of a ro-vibrational CO 2 transition.Frequency counting with respect to an OFCS takes to a relative precision of 5 parts in 10 11 .Saturated-absorption spectroscopy provides a narrow and stable reference, and the final result is a remarkable improvement (a factor 30) compared with the Doppler-limited frequency measurements reported in our previous work [24].Although not effective in narrowing the laser linewidth, the frequency lock to this reference allows to overcome the previous limitations due to the free-running low-frequency fluctuations of our QCL source, thus enabling long-time-averaging measurements of the frequency with the consequent statistical reduction of the uncertainty.
In Section 2 we describe our saturated-absorption experiment, based on an original set-up allowing the efficient exploitation of most of the QCL available power for both the spectroscopy and the non-linear frequency generation.In Section 3 the first-derivative locking scheme is briefly treated.Section 4 is finally dedicated to the analysis of the resulting beat note and its counting for the absolute frequency measurement of the molecular transition.

Sub-Doppler spectroscopy of CO 2 with a QCL
In Fig. 1 a simplified schematic of the experimental set-up is shown, describing mainly the optical layout used for saturated-absorption spectroscopy.We have used a single-mode distributedfeedback (DFB) QCL emitting at 4.3 μm and operating at cryogenic temperatures.The QCL has a quite low threshold current (about 100 mA at 86 K) and a frequency tunability with current of 400 MHz/mA; it is housed in a liquid-N 2 -cooled dewar and is connected to a low-noise current driver.Since the electrical isolation of the current driver is not sufficient to reject additional noise coming from the AC line, which induces a spurious modulation of the QCL frequency, we adopt an UPS battery supply for powering the current driver.
Before being sent to the cell, the laser beam is collimated and size-reduced by a telescope as previously described in [24].In order to perform sub-Doppler spectroscopy with two counterpropagating beams while avoiding undesired optical feedback to the laser, we have used two Fig. 1.Schematic of the experimental set-up.In the figure the main blocks of the apparatus have been highlighted by dashed lines: the QCL housing and collimation (a), the saturation spectroscopy set-up (b), the SFG assembly (c), the near-IR lasers phase-locked to the comb (d) and the beat-note detection and measurement (e).P1 and P2 are wire grid polarizers, T-λ /2 is a tunable half-waveplate and BS is a beam-splitter.crossed wire-grid polarizers (P1 and P2 in the figure).The p-polarized QCL beam passes through a half-waveplate, which rotates its polarization by few degrees.The first polarizer (P1) transmits the p-polarized fraction of the beam (about 80% of the total power) while reflecting the s-polarized part.The former acts in the absorption cell as the "pump" beam for the CO 2 transition, is totally reflected by the second polarizer (P2) and reused in the next section of the experiment (the SFG process).The latter beam, transmitted by P2, acts in the cell as the "probe" radiation and is totally reflected by P1 to be finally detected onto a liquid-N 2 -cooled HgCdTe biased photoconductive detector (1.5 MHz bandwidth).Despite the lack of mid-IR optical isolators, this solution allows us to have a full control on the counter-propagating beams overlap and focusing while avoiding optical feedback onto the laser.The absorption cell is 12 cm long and has AR-coated CaF 2 windows.Thanks to the ability of independently focusing the two beams, we have adjusted the diameter of the probe beam in order to make it smaller than the pump beam along the whole cell, thus ensuring a high contrast of the saturation signal.The detector is connected to a home-made voltage preamplifier provided with DC/AC-coupled outputs: these two channels allow us to continuously monitor the absorption signal level (DC output) while using the AC signal for the feedback loop to the laser.
Due to the long open-air path of the laser beam before the cell (about 1.5 m), we suffer strong absorption from atmospheric CO 2 molecules.In order to have a good compromise between a suitable ro-vibrational transition strength for saturation spectroscopy and low absorption in air, the hot-band (01 1 1 − 01 1 0) P(30) CO 2 transition has been chosen.The transition center frequency and linestrength, as reported in the HITRAN database [25], are ν=2310.5062cm −1 and S=6.6×10 −20 cm respectively.The QCL working temperature is 86.00K and the corresponding driving current is 170 mA.The pump beam power incident upon the CO 2 sample is about 2 mW, leading to an intensity of 160 W/m 2 ; this is a factor 2 greater than the saturation intensity Fig. 2. Saturation spectrum of the (01 1 1 − 01 1 0) P(30) CO 2 transition in direct-absorption (a) and first-derivative detection (b).The gas pressure in the cell was 20 mTorr (which brings to a relative absorption of about 10%) and the pump intensity interacting with the gas sample was about a factor 2 greater than the saturation level.The two traces have been recorded by a digital scope, with a sweeping time of about 0.2 seconds.The first-derivative signal was obtained by a lock-in amplifier with 1 ms integration time constant.The best fit and residuals are also shown. of 80 W/m 2 , calculated for our gas pressure (20 mTorr) and the P(30) transition dipole moment (5.09 × 10 −2 D) according to [26].We point out that, depending on the laser linewidth, this intensity may not lead to a strong saturation regime.
The saturation signal has been first observed in direct absorption, by continuously scanning the laser frequency with a slow (few Hz) saw-tooth modulation of the laser current.Figure 2(a) shows a trace recorded by a digital scope: the well contrasted Lamb dip (13% contrast factor) shows a HWHM of about 5 MHz.Wavelength modulation spectroscopy is then implemented at 40 kHz rate, with a modulation depth of about 3.5 MHz: this value has been chosen in order to have the largest first-derivative signal without broadening the dip.The AC channel of the detector preamplifier is sent to an analog lock-in amplifier for demodulation.Figure 2(b) shows a first-derivative saturated-absorption spectrum recorded in the same experimental conditions as in Fig. 2(a).The best fit of the experimental data has been obtained with a convolution between two Gaussian functions (accounting for both the Doppler profile and the Lamb dip).The Lamb-dip HWHM resulting from the fit is about 5.3 MHz.
From the HITRAN database the pressure-broadening coefficient is about 3.5 MHz/Torr.The expected contributions of both pressure and transit-time broadening to the Lamb-dip width (HWHM) are about 70 kHz and 100 kHz respectively [26]: both are negligible with respect to the measured HWHM.For this reason the measured Lamb-dip width can be attributed to the free-running QCL frequency jitter (as confirmed by further measurements reported below: see figure 4).

Frequency locking to the Lamb dip
From preliminary measurements on the laser frequency noise (following the method used in Ref. [27]) it results that there is a 1/ f type noise dominating for f < 100 kHz that does not arise from the driver current noise: it thus can be corrected by a feedback loop on the current driver itself.Among the sources of this additional noise we mention temperature fluctuations, that are responsible for all the slow frequency drifts and that, if not compensated, strongly disturb the measurement, as we will see in the next section.We used the first-derivative saturation dip as the error signal to lock the QCL frequency to the transition center.The lock-in output is processed by a home-made PID controller, and the feedback signal is sent to the modulation input of the current driver.During operation in locked mode, the stability of the optical alignment is monitored by checking the absorption signal from the DC channel of the detector preamplifier.
Figure 3(a) shows a comparison between the frequency noise power spectral density of the QCL in both locked and unlocked modes.A noise reduction exceeding 20 dB at frequencies lower than 30 Hz is obtained; it is also evident the cut-off introduced by the lock-in time constant, set to its minimum available value of 1 ms.The reduction of the slow frequency fluctuations is qualitatively presented in Fig. 3(b), where the lock-in output, in locked and unlocked conditions, is shown.
Because of the small bandwidth, the loop is unable to reduce the laser high-frequency jitter.However, the advantage brought on the precision of our frequency measurements, which mainly require a long-term stability, is evident (as shown later in Fig. 5(a)).

Absolute frequency measurements of the CO 2 saturated transition
After interaction with the gas, the pump beam reflected by the polarizer P2 is available for the second stage of the experiment: it is superimposed to the beam of a fiber-amplified Nd:YAG laser by a diffraction grating and then sent to a non-linear crystal for the sum-frequency generation of light at 854 nm.The set-up is similar to that described in [24]: the non-linear crystal is a 40-mm-long PPLN crystal with a poling period of 22.8 μm chosen to achieve phase matching at nearly room temperature.The crystal temperature is stabilized at 17 • C within 1 mK by using a Peltier element controlled by PID electronics.Despite the fact that the pump beam contains 80% of the total power, the combination of several loss effects (absorption from air and in the cell, reflections from the uncoated surfaces of the polarizers and the half-waveplate), makes the QCL radiation available for the SFG process to be about 1/3 of the original power.The maximum generated near-IR power at the crystal output in working conditions (laser resonant with the CO 2 transition and locked to the Lamb dip) is about 3 μW.After the PPLN crystal an interference filter centered at 850 nm filters out both residual QCL and Nd:YAG beams and transmits only the SFG radiation, which is then collimated and superimposed to the beam of an external-cavity diode laser emitting at a frequency 150 MHz apart.A fast avalanche photodiode finally detects the resulting beat note Δν, with a 40 dB signal-to-noise ratio (in a 400 kHz resolution bandwidth).
Both the Nd:YAG laser and the diode laser are referenced to an OFCS operating in the 500 ÷ 1100 nm region, with a repetition rate of about 1 GHz, based on a mode-locked femtosecond Ti:sapphire laser [6].The locking scheme is an upgrade of that already described in [24], and results in an actual phase lock between the two lasers, with the comb behaving as a transfer oscillator [28].This cancels out all the phase-noise contributions from the Nd:YAG, the diode laser and the comb in the detected beat-note, whose linewidth is due to the QCL only.The beatnote has been acquired with a real-time spectrum analyzer, and its spectral profile has been studied over different time scales, ranging from 40 μs to few tens of ms.As expected from the performances of our slow frequency-lock loop, we observe a few-MHz-broad fast jitter with a quite irregular profile, which fades into a regular Gaussian profile when averaged over longer time scales.As an example, Fig. 4 shows the comparison of the spectral profiles obtained by FFT of two data streams of different lengths, with the QCL locked to the Lamb dip. .From this comparison we can conclude that the residual frequency jitter of the laser is the crucial issue that limits the resolution of our experiment.Moreover, the Gaussian profile of the frequency-noise distribution suggests that, on time scales longer than few tens of μs, a random noise source is still predominant and masks both the Lorentzian intrinsic linewidth of the QCL emission and the natural linewidth of the Lamb dip.At the same time, the random nature of the frequency fluctuations ensures that a statistical average of the frequency counts can lead to the determination of its "true" value.
In order to perform absolute frequency measurements, the beat-note signal is amplified up to 0 dBm level to be properly measured by a frequency counter.The CO 2 transition center frequency ν C can be thus easily obtained by the following relation: where ν D and ν Y are the frequencies of the comb-referenced diode laser and Nd:YAG laser, respectively.Each measurement session consisted in consecutive 1 s gate-time countings of the beat-note frequency.The data stream was acquired by a PC via a GPIB interface.Each session lasted several minutes, and was stopped only when some instabilities occurred in the locking of any of the lasers.Between two consecutive sessions, the optimization of the three lasers locking and, eventually, of the spectroscopy alignment was performed.Each data set yields the mean frequency value Δν with the associated uncertainty (standard deviation of the mean).Following this procedure, we have acquired 53 data sets over a period of 2 weeks.As an example, Fig. 5(b) shows a 20 minutes long data set.As we can see, the acquisition is affected by slow drifts and oscillations, which can be mainly ascribed to the presence of residual optical interference fringes that shift the locking point by adding a variable background to the derivative signal.Such unwanted are barely visible in the typical timescale of a single acquisition, but are much more evident when comparing two different data sets.They give the main contribution to the uncertainty budget of our measurements.Since, at present, it is not possible to fully control these effects, we have tried to convert the systematic error into a statistical one.This has been done by changing the optical alignment between a measurement session and the next one, thus randomly modifying the free-spectral range of the spurious etalon effects.A second systematic error contribution arises from the non-zero background of the derivative signal due to small asymmetries of the Doppler profile with respect to the Lamb dip.We have provided a precise offset regulation at the PID input in order to cancel out this effect, so that it can be neglected as compared to the statistical uncertainty.
The contribution of all these effects is clearly visible in Fig. 6, where the Δν values and uncertainties obtained from the complete set of measurement sessions are summarized.Although the error associated to a single mean value is of only few kHz, the final uncertainty in determining the transition absolute frequency is limited by the repeatability of the measurements, as the spread of the points clearly shows.For this reason we adopt the standard deviation as a safer estimate of the final frequency uncertainty.The 3.5 kHz average value of the errors associated to the measurements can be assumed as a reasonable estimate for the ultimate precision (5 parts in 10 11 ) achievable in the absence of all the systematics.Fig. 6.All the measured beat-note frequencies are reported in this figure.Each point corresponds to the mean value of a long-time acquisition (as that shown in Fig. 5), with its uncertainty (standard deviation of the mean).The mean value and standard deviation of the data are also shown (red line and grey area, respectively).
The average of all the Δν points gives the best value of 149.538MHz for the beat-note frequency, with a 75 kHz standard deviation.As both ν D and ν Y can be measured with a precision well below the kHz level, by using Eq.( 1

Conclusion
In conclusion, a liquid-N 2 -cooled cw DFB QCL emitting at 4.3 μm has been used for saturation spectroscopy of CO 2 .The Lamb dip has been recorded both in direct absorption (with a contrast of about 13%) and in first derivative (by using a lock-in amplifier).The measured dip width (5.3 MHz HWHM over tens of ms timescales) cannot be explained in terms of collisional and transit-time broadening but is ascribed to the QCL frequency jitter.The first-derivative dip signal has been used to stabilize the QCL frequency to the transition center.The locking loop allows a significant frequency-noise reduction below 1 kHz, which removes the slow fluctuations but is not suitable for a reduction of the QCL fast jitter.Thanks to a SFG process with a Nd:YAG laser in a PPLN crystal, the QCL stabilized frequency has been compared with that of a diode laser emitting at 854 nm.As both the Nd:YAG and diode lasers are phase-locked to an OFCS, the absolute frequency of the observed CO 2 transition can be measured.Thanks to the locking-loop, several long-time measurements of the Lamb-dip frequency have been acquired over a period of 2 weeks, with a relative short-term precision of 5 parts in 10 11 (3.5 kHz) and an overall uncertainty of 75 kHz limited by systematics.By improving the frequency-lock performances up to the levels already obtained by other groups [15], an ultimate precision only limited by the comb stability (parts in 10 13 for our setup) is in principle achievable, assuming a complete control on all the systematic error sources.This requires a completely different servo electronics and a proper coupling of the correction signal to the laser chip.
The ability of measuring a transition frequency with such a precision can be of great importance, since it may allow to define, in the spectral region covered by QCLs, a set of molecular lines forming an inexpensive grid of secondary frequency standards, suitable for applications requiring relative accuracies in the 10 −12 ÷ 10 −13 range.Moreover, thanks to the drastic reduction of the uncertainty with respect to the HITRAN database, performing frequency measurements on a set of transitions of the same molecule will allow to determine the related set of molecular parameters with an improved accuracy.

Fig. 3 .
Fig. 3. (a) QCL noise power spectral density in free-running (red trace) and locking (black trace) conditions, obtained by using the slope of a germanium-etalon transmission fringe as a frequency discriminator.(b) The lock-in output signal qualitatively shows the frequency fluctuations that can be compensated by the loop.

Fig. 4 .
Fig. 4. Power spectral density of the beat-note between the SFG and the diode laser radiation recorded with real-time spectrum analyzer.The acquisition lengths are 70 ms (black Gaussian profile) and 70 μs (grey line).A Gaussian function has been fitted to the black spectrum and the obtained is 5.3 MHz.

Fig. 5 .
Fig. 5. (a) Comparison between the spreads of the beat-note frequency values as measured by the counter in free-running and locked conditions.(b) 20-minutes-long acquisition of the beat-note frequency, shown in a 100× zoomed scale.The right part of the figure shows the frequency distribution of the data: a Gaussian fit is superimposed and the resulting 2 kHz standard deviation of the mean can be assumed as the precision of this measurement.
) we can obtain the absolute measurement of the transition center frequency ν C as ν C = 69 267 227.764 (75) MHz (2) With 20 mTorr of CO 2 in the cell the contribution to ν C given by the pressure shift is about 2 kHz [29], well within the uncertainty.The obtained value agrees with the frequency reported by the HITRAN database (ν = 69 267 233 MHz with a 3÷30 MHz error) improving the uncertainty by two orders of magnitude.(C) 2008 OSA 21 July 2008 / Vol.16, No. 15 / OPTICS EXPRESS 11645