  The Terahertz frequency range bears intriguing opportunities, beyond very
advanced applications in spectroscopy and matter control. Peculiar quantum
phenomena are predicted to lead to light emission by non-trivial mechanisms.
Typically, such emission mechanisms are unraveled by temporal correlation
measurements of photon arrival times, as demonstrated in their pioneering work
by Hanbury Brown and Twiss. So far, the Terahertz range misses an experimental
implementation of such technique with very good temporal properties and high
sensitivity. In this paper, we propose a room-temperature scheme to measure
photon correlations at THz frequencies based on electro-optic sampling. The
temporal resolution of 146 fs is faster than one cycle of oscillation and the
sensitivity is so far limited to ~1500 photons. With this technique, we measure
the photon statistics of a THz quantum cascade laser. The proposed measurement
scheme allows, in principle, the measurement of ultrahigh bandwidth photons and
paves the way towards THz quantum optics.
