Time-resolved statistics of nonclassical light in Josephson photonics

Abstract

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 ${g}^{(2)}(\ensuremath{\tau})$ and the waiting-time distribution $w(\ensuremath{\tau})$. 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 nonclassical 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 ${g}^{(2)}(\ensuremath{\tau})$ and $w(\ensuremath{\tau})$ as well as the specific information which is provided by each of them.