Statistics of radiation at Josephson parametric resonance

I have not written to the blog for about a month. A fact which is not a direct consequence of this, but related to this is that Ciprian, Fabian Hassler and me have finally accomplished a long paper entitled as above. You can find it on the Arxiv.

The topic is hot, and the paper could have been short, yet we have discovered on time that a part of our results have been already obtained in optical context.

The abstract is as follows:Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation.
To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts each encompassing 2N photons, this accounts for the bunching of the photon pairs produced in course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.

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