  Quantum mechanics ascribes to the ground state of the electromagnetic
radiation zero-point electric field fluctuations that permeate empty space at
all frequencies. No energy can be extracted from the ground state of a system
and, therefore, these fluctuations cannot be measured directly with an
intensity detector. The experimental proof of their existence came thus from
more indirect evidence, such as the Lamb shift, the Casimir force between close
conductors or spontaneous emission. A direct method to determine the spectral
characteristics of vacuum field fluctuations has been missing so far. In this
work, we perform a direct measurement of the field correlation on these
fluctuations in the terahertz frequency range using electro-optic detection in
a non-linear crystal placed in a cryogenic environment. We investigate their
temporal and spatial coherence, which, at zero time delay and spatial distance,
has a peak value of $6.2\cdot 10^{-2}~V^2/m^2$, corresponding to a fluctuating
vacuum field of 0.25 V/m. With this measurement, we determine the spectral
composition of the ground state of electromagnetic radiation which lies within
the bandwidth of electro-optic detection.
