Quantum cascade laser frequency comb locked with 200 mrad residual phase noise

. Using near-infrared light, we tightly-lock a mid-infrared quantum cascade laser frequency comb to another laser, achieving a residual integrated phase noise of 200 mrad. This high coherence is pertinent for highly-sensitive dual-comb spectroscopy and metrology.


Introduction
Quantum cascade lasers (QCLs) are a unique source of high-power and large repetition-rate frequency combs for the mid-infrared (MIR) [1].QCL combs are mainly exploited for dual-comb spectroscopy, but other applications of interest are accurate frequency calibration [2] and synthesis.However, this requires high spectral purity, which demands a fast stabilization scheme.Drive current is a conventional handle to modulate the QCL with bandwidths reaching up to 400 kHz [3].Alternatively, light at another wavelength could control the QCL comb [4] as already demonstrated for THz QCL combs [5].In this work, we take advantage of the mature near-infrared (NIR) technology to tightly-lock a MIR QCL comb to a distributed feedback (DFB) QCL using a NIR laser with a record stabilization bandwidth of 2 MHz and reach an integrated residual phase noise as low as 200 mrad.We believe that these results are important for dual comb spectroscopy and frequency metrology in the MIR.

Experimental setup
The setup is schematized in Fig. 1.A QCL fabricated at ETH Zurich emits a frequency comb in the 8 μm wavelength-range with a mode-spacing of approximately 11 GHz.The comb is heterodyned with a DFB-QCL (Alpes Laser) on a fast photodetector.The beat signal at 240 MHz is amplified and divided by 4, resulting in a 60 MHz signal that is mixed in a double balanced mixer with a reference RF signal.The low-passed mixing product reproduces the phase between one comb line and the DFB-QCL divided by 4 and is input to two servo-controllers (D2-125, Vescent) to correct the comb line frequency.In parallel, the repetition frequency is phase locked by RF injection locking with 15 dBm of RF power [6].* e-mail: kenichi.komagata@unine.chOne servo controller acts on the drive current (electrical actuation).The other controller is high passed at 1 kHz and modulates the intensity of a NIR DFB laser emitting on average 2 mW at 1530 nm through the integrated electro-absorption modulator (EAM).This light is directed to the front facet of the QCL comb by a customdesigned dichroic mirror (DM).We measure the beat note with a phase noise analyzer (R&S, FSWP26) to assess the performances of the lock with and without actuation of the NIR continuous wave (CW) laser.

Results
Optimizing the lock servo-controllers, we obtain the phase noise power spectral density (PSD) shown in blue in Fig. 2(a).It remains below or close to -80 dBc/Hz for all measured Fourier frequencies (1 Hz to 5 MHz).A first small bump near 3 kHz is due to the interference between the electrical and optical actuation.Then a second broad bump between 100 kHz and 500 kHz shows the suppression of the additional noise generated by the electrical lock.The last bump, above 2 MHz, shows the servo bandwidth.As a result the integrated phase noise from 5 MHz to 1 Hz is 200 mrad, mainly stemming from the second and third bumps.The residual phase noise is improved by a factor 10 compared to the electrical actuation alone (orange line), and the actuation bandwidth by a factor 6. We note that for the electrical lock alone, the division had to be increased from 4 to 15 to avoid phase-slips, whereas with optical actuation, the bandwidth was fast enough to avoid them.
In terms of power spectrum, the beat note shows an increase in power by 21 dB while the pedestal is reduced by 15 dB, as shown in Fig. 2(b).The resulting signalto-noise (SNR) with respect to the pedestal is 50 dB in a 100 Hz resolution bandwidth.

Conclusion
We have demonstrated the tight-locking of a MIR QCL frequency comb to an auxiliary laser with a bandwidth above 2 MHz and a residual integrated phase noise of 200 mrad.This leads to an increase of SNR by 35 dB in a 100 Hz resolution bandwidth.With the parallel phaselock of the repetition frequency by RF injection, we thus show that QCL frequency combs can operate with high frequency purity and could be used for a variety of applications that require low-noise, such as coherently-averaged dual-comb spectroscopy [7] and MIR metrology [2].

Figure 1 .
Figure 1.Setup for the stabilization of a MIR QCL frequency comb to a DFB QCL using NIR light modulated by an electroabsorption modulator (EAM).In parallel, the repetition frequency is phase-locked by RF injection locking.

Figure 2 .
Figure 2. Results of the stabilization.(a) Phase noise power spectral density (PSD) of one comb line in the free-running case (green), with stabilization through the drive current (orange), and with the NIR light in addition (blue).The inset shows the integrated phase noise φ rms integrated from 5 MHz to f cut .(b) Electrical spectrum of the stabilized beat note in a 100 Hz resolution bandwidth (RBW), where the colors follow from (a).