  Due to its fast and high resolution characteristics, dual-comb spectroscopy
has attracted an increasing amount of interest since its first demonstration.
In the terahertz frequency range where abundant absorption lines (finger
prints) of molecules are located, multiheterodyne spectroscopy that employs the
dual-comb technique shows an advantage in real-time spectral detection over the
traditional Fourier transform infrared or time domain spectroscopies. Here, we
demonstrate compact terahertz dual-comb spectroscopy based on quantum cascade
lasers (QCLs). In our experiment, two free-running QCLs generate approximately
120 GHz wide combs centered at 4.2 THz, with slightly different repetition
frequencies. We observe that $\sim$490 nW terahertz power coupling of one laser
into the other suffices for laser-self-detecting the dual-comb spectrum that is
registered by a microwave spectrum analyzer. Furthermore, we demonstrate
practical terahertz transmission dual-comb spectroscopy with our device, by
implementing a short air path at room temperature. Spectra are shown of
semiconductor samples and of moist air, the latter allowing rapid monitoring of
the relative humidity. Our devices should be readily extendable to perform
imaging, microscopy and near-field microscopy in the terahertz regime.
