  The interplay of the tunneling transfer of charges and the emission and
absorption of light can be investigated in a set-up, where a voltage-biased
Josephson junction is placed in series to a microwave cavity. Here, we
concentrate on the emission process and show that due to the inherent
nonlinearity of the Josephson junction tunneling Cooper-pairs can create a
variety of non-classical states of light. Depending on experimental parameters
and tuning the device can be described by effective Hamiltonians, indicating
specific photon creation mechanisms which lead to strongly bunched or
anti-bunched light emission. We derive explicit analytical expressions for the
photon correlation function $g^{(2)}(\tau=0)$ for these different processes and
investigate their full crossover numerically. Photon distribution functions
show squeezing and other interesting non-Poissonian behavior.
