Time-resolved statistics of nonclassical light in Josephson photonics

The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a setup, where a voltage-biased Josephson junction is connected in series with a microwave cavity. We focus here on the emission processes of photons and analyze the underlying time-dependent statistics using the second-order correlation function $g^{(2)}(\tau)$ and the waiting-time distribution $w(\tau)$. Both observables highlight the crossover from a coherent light source to a single-photon source. Due to the nonlinearity of the Josephson junction, tunneling Cooper pairs can create a great variety of non-classical states of light even at weak driving. Analytical results for the weak driving as well as the classical regime are complemented by a numerical treatment for the full nonlinear case. We also address the question of possible relations between $g^{(2)}(\tau)$ and $w(\tau)$ as well as the specific information which is provided by each of them.