Electronic and photonic counting statistics as probes of non-equilibrium quantum dynamics

Abstract

Abstract We analyse the full counting statistics (FCS) of photons flowing in and out of a microwave cavity coupled to a voltage-biased Josephson junction. Tunnelling of Cooper pairs generates a coherent flow of photons into the cavity whilst at the same time photons can also leak out incoherently. We use a very general unitary transformation method to demonstrate that there is a simple connection between the FCS of the charges and the photons in the long time limit, revealing that all the cumulants of the coherent and the incoherent processes match in that limit. We also explore some of the interesting features in the counting statistics of the charges and photons which arise from the strongly nonlinear dynamics of the system. These include very narrow distributions associated with the emergence of coherent transport and regimes where counting of either an odd or an even number of photons leaving the cavity can result in strongly non-classical cat states within the cavity.