Quantum cascade laser frequency stabilization at the sub-Hz level

Journal name:
Nature Photonics
Year published:
Published online


High-precision measurements with molecules may refine our knowledge of various fields of physics, from atmospheric and interstellar physics to the standard model or physics beyond it. Most of them can be cast as absorption frequency measurements, particularly in the mid-infrared ‘molecular fingerprint’ region, creating the need for narrow-linewidth lasers of well-controlled frequency. Quantum cascade lasers provide a wide spectral coverage anywhere in the mid-infrared, but show substantial free-running frequency fluctuations. Here, we demonstrate that the excellent stability and accuracy of an ultra-stable near-infrared laser, transferred from a metrological institute through a fibre link, can be copied to a quantum cascade laser using an optical frequency comb. The obtained relative stability and accuracy of 2 × 10−15 and 10−14 exceed those demonstrated so far with quantum cascade lasers by almost two orders of magnitude. This set-up enables us to measure molecular absorption frequencies with state-of-the-art uncertainties, confirming its potential for ultra-high-precision spectroscopy.

At a glance


  1.  Experimental set-up.
    Figure 1:  Experimental set-up.

    The NIR frequency reference, νref, generated at LNE-SYRTE with ultra-stable (US) laser #1 is transferred to LPL through a 43-km-long optical-fibre link. Its absolute frequency is measured against primary frequency standards by the use of an OFC (SYRTE-OFC). Its stability is provided by an ultra-stable cavity (see Methods) whose frequency drift is removed by an acousto-optic modulator (AOM). At LPL, the comb repetition rate, frep, of an OFC is phase-locked onto this reference. The QCL is then phase-locked onto a harmonic of frep by performing sum-frequency generation in an AgGaSe2 crystal (see Methods). The beat note of frequency Δ1 is processed to generate the error signal for the QCL phase-lock loop (PLL). The signal of frequency Δ1′ on photodiode PD1 corresponds to the beat note between the MIR reference and a multiple of frep and the signal of frequency Δ2 on photodiode PD2 corresponds to the beat note between the MIR reference and the QCL. The stabilities and frequency noise PSDs are evaluated by using a counter and a fast Fourier transform (FFT) analyser. Arrows indicate movable optics and the padlocks symbolize the OFCs' phase-lock loops. Ultra-stable laser #2 is used to evaluate the spectral purity of the LPL comb.

  2. Assessment of the QCL frequency stability.
    Figure 2: Assessment of the QCL frequency stability.

    Fractional frequency stability of the beat note between the QCL phase-locked onto the NIR reference (QCL/OFC) and the MIR reference (curve a, red squares), the beat note between the MIR reference and the OFC (curve b, blue circles), the OFC (curve c, green triangles) and the beat note between the QCL and the CO2 laser, both stabilized onto the OFC (curve d, black stars). Overlapping Allan deviations are processed from data measured using a Λ-type counter with 1 s gate time. For curve d, a dead-time free counter was used.

  3. Characterization of frequency noises.
    Figure 3: Characterization of frequency noises.

    Frequency noise PSD of the beat note between the QCL phase-locked onto the NIR reference (QCL/OFC) and the MIR reference (curve a, red), the beat note between the MIR reference and the OFC (curve b, blue), the OFC (curve c, green), the noise-compensated 43 km optical-fibre link (curve d, brown) and the free-running QCL (curve e, black). All these PSDs are relative to a carrier frequency of 29.1 THz (10.3 µm wavelength).

  4.  QCL line shape and beat note with the MIR reference.
    Figure 4:  QCL line shape and beat note with the MIR reference.

    a, Calculated QCL line shape showing a 0.2 Hz FWHM (10 mHz resolution bandwidth). This estimation is based on the temporal data used to derive the OFC relative stability (curve c of Fig. 2) and the OFC frequency noise PSD (curve c of Fig. 3). b, Beat note between the QCL phase-locked onto the NIR reference and the MIR reference, recorded with a FFT analyser (125 mHz resolution, average of 10 sweeps of 8 s). The beat note is offset to zero by subtracting ∼50 kHz. The red line is a Lorentzian fit of the data with a linewidth (FWHM) of 10 Hz.

  5.  OsO4 spectrum, in the vicinity of the R(14) emission line of CO2.
    Figure 5:  OsO4 spectrum, in the vicinity of the R(14) emission line of CO2.

    Two lines are recorded over a span of 5 MHz in steps of 5 kHz, using third harmonic detection. The x axis is offset by νOsO4/R(14) = 29,137,747,033,333 Hz, corresponding to the reported absolute frequency of the OsO4 reference line (left-hand line)39. The right-hand line has not yet been reported in the literature. Inset: spectrum of the reference line recorded over 200 kHz in steps of 1 kHz. These data are fitted to the sum of a third and fifth derivative of a Lorentzian.


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Author information


  1. Laboratoire de Physique des Lasers, Université Paris 13, Sorbonne Paris Cité, CNRS, 99 Avenue Jean-Baptiste Clément, Villetaneuse 93430, France

    • Bérengère Argence,
    • Bruno Chanteau,
    • Olivier Lopez,
    • Christian Chardonnet,
    • Christophe Daussy,
    • Benoît Darquié &
    • Anne Amy-Klein
  2. LNE-SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, 61 Avenue de l'Observatoire, Paris 75014, France

    • Daniele Nicolodi,
    • Michel Abgrall &
    • Yann Le Coq


B.A., B.C., O.L., Y.L.C. and A.A.K. conceived and designed the experiment. B.A., B.C., D.N., B.D. and A.A.K. performed the experiment. B.A., O.L., D.N., M.A., C.D., B.D., Y.L.C. and A.A.K. analysed the data. B.A., M.A., B.D., Y.L.C. and A.A.K. contributed materials/analysis tools. All authors discussed the results. B.A., O.L., D.N., M.A., C.C., C.D., B.D., Y.L.C. and A.A.K. wrote the paper.

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