  There exists a fascinating dual representation of the electric ac current
flowing through a normal conductor. On the one hand, it can be understood in
terms of charge transport. On the other hand, it consists in an electomagnetic
field guided by conducting structures embedded in an insulator. The former
point of view, in its quantum version, is particularly adapted to describe the
electron shot noise in a coherent conductor, like a tunnel junction at
ultra-low temperature. However, when the junction is appropriately biased by a
dc and an ac voltage, the noise it generates is best analyzed using the latter
representation and the tools of quantum optics, as the radiation exhibits clear
signs of non-classicality. Herein, we report the measurement of the statistics
of photons emitted by such a tunnel junction. We observe a photon shot noise
characteristic of photon pair emission, as its Fano factor for small signal is
above unity. The theory of electron shot noise, dealing exclusively with the
tunneling of charges through the junction, quantitatively fits the data from
which photon shot noise is extracted. This experiment thus provides a clear
link between the dual representations.
