  Optical frequency comb synthesizers (FCs) [1] are laser sources covering a
broad spectral range with a number of discrete, equally spaced and highly
coherent frequency components, fully controlled through only two parameters:
the frequency separation between adjacent modes and the carrier offset
frequency. Providing a phase-coherent link between the optical and the
microwave/radio-frequency regions [2], FCs have become groundbreaking tools for
precision measurements[3,4].
  Despite these inherent advantages, developing miniaturized comb sources
across the whole infrared (IR), with an independent and simultaneous control of
the two comb degrees of freedom at a metrological level, has not been possible,
so far. Recently, promising results have been obtained with compact sources,
namely diode-laser-pumped microresonators [5,6] and quantum cascade lasers
(QCL-combs) [7,8]. While both these sources rely on four-wave mixing (FWM) to
generate comb frequency patterns, QCL-combs benefit from a mm-scale
miniaturized footprint, combined with an ad-hoc tailoring of the spectral
emission in the 3-250 {\mu}m range, by quantum engineering [9].
  Here, we demonstrate full stabilization and control of the two key parameters
of a QCL-comb against the primary frequency standard. Our technique, here
applied to a far-IR emitter and open ended to other spectral windows, enables
Hz-level narrowing of the individual comb modes, and metrological-grade tuning
of their individual frequencies, which are simultaneously measured with an
accuracy of 2x10^-12, limited by the frequency reference used. These
fully-controlled, frequency-scalable, ultra-compact comb emitters promise to
pervade an increasing number of mid- and far-IR applications, including quantum
technologies, due to the quantum nature of the gain media [10].
