Input-output description of microwave radiation in the dynamical Coulomb blockade

We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input–output formalism for the radiation field is established, using a perturbation expansion in the junction’s critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy–Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region. 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 16 (2014) 015015 1367-2630/14/015015+27$33.00 © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft New J. Phys. 16 (2014) 015015 J Leppäkangas et al