  We analyze the creation and emission of pairs of highly nonclassical
microwave photons in a setup where a voltage-biased Josephson junction is
connected in series to two electromagnetic oscillators. Tuning the external
voltage such that the Josephson frequency equals the sum of the two mode
frequencies, each tunneling Cooper pair creates one additional photon in both
of the two oscillators. The time-resolved statistics of photon emission events
from the two oscillators is investigated by means of single- and
cross-oscillator variants of the second-order correlation function
$g^{(2)}(\tau)$ and the waiting-time distribution $w(\tau)$. They provide
insight into the strongly correlated quantum dynamics of the two oscillator
subsystems and reveal a rich variety of quantum features of light including
strong antibunching and the presence of negative values in the Wigner function.
