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

Understand

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.