We present an experimental investigation of the multimode dynamics and the coherence of terahertz quantum cascade lasers emitting over a spectral bandwidth of ~1THz. The devices are studied in free-running and under direct RF modulation. Depending on the pump current we observe different regimes of operation, where RF spectra displaying single and multiple narrow beat-note signals alternate with spectra showing a single beat-note characterized by an intense phase-noise, extending over a bandwidth up to a few GHz. We investigate the relation between this phase-noise and the dynamics of the THz modes through the electro-optic sampling of the laser emission. We find that when the phase-noise is large, the laser operates in an unstable regime where the lasing modes are incoherent. Under RF modulation of the laser current such instability can be suppressed and the modes coherence recovered, while, simultaneously, generating a strong broadening of the THz emission spectrum.
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