Time-resolved statistics of photon pairs in two-cavity Josephson photonics

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.