  Mode-locking operation and multimode instabilities in Terahertz (THz) quantum
cascade lasers (QCLs) have been intensively investigated during the last
decade. These studies have unveiled a rich phenomenology, owing to the unique
properties of these lasers, in particular their ultrafast gain medium. Thanks
to this, in QCLs a modulation of the intracavity field intensity gives rise to
a strong modulation of the population inversion, directly affecting the laser
current. In this work we show that this property can be used to monitor in
real-time the temporal dynamics of multimode THz QCLs, using a self-detection
technique combined with a broadband real-time oscilloscope. We study a 4.2THz
QCL operating in free-running, and observe the formation of current pulses
associated with trains of self-mode-locked optical pulses. Depending on the
current pumping we find alternating regimes of unstable and stable pulse
trains, respectively at the fundamental cavity repetition rate and its second
harmonic. We interpret these measurements using a set of effective
semiconductor Maxwell-Bloch equations that qualitatively reproduce the
fundamental features of the laser dynamics, and also provide evidence in
support of the solitonic nature of the observed pulses.
