A widely tunable 10-$mu$m quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy

We report the coherent phase-locking of a quantum cascade laser (QCL) at 10-$mu$m to the secondary frequency standard of this spectral region, a CO2 laser stabilized on a saturated absorption line of OsO4. The stability and accuracy of the standard are transferred to the QCL resulting in a line width of the order of 10 Hz, and leading to our knowledge to the narrowest QCL to date. The locked QCL is then used to perform absorption spectroscopy spanning 6 GHz of NH3 and methyltrioxorhenium, two species of interest for applications in precision measurements.