Josephson radiation in a superconductor-quantum dot-superconductor junction

We investigate the Josephson radiation emitted by a junction made of a quantum dot coupled to two conventional superconductors. At strong coupling, such a junction accommodates two Andreev bound states, which are slightly detached from the continuum outside the superconducting gap. Furthermore, when the dot is tuned close to resonance, the residual backscattering opens a small gap near the Fermi energy between the discrete states. Under voltage bias, we formulate a stochastic model that accounts for nonadiabatic processes, which change the occupations of the Andreev bound states. This model allows one to calculate the current noise spectrum and determine the Fano factor. Analyzing the finite-frequency noise, we find that the model may exhibit either an integer or a fractional AC Josephson effect, depending on the bias voltage and the size of the gaps in the Andreev spectrum. Our results assess the limitations in using the fractional Josephson radiation as a probe of topological superconductivity.