Noise characteristics of the current biased super-semi Josephson junctions

Josephson junctions with a semiconductor weak link demonstrated high tunability suitable for applications in superconducting quantum devices. 

At the same time, the noise and dissipation characteristics of these Junctions remain unexplored. We present a theoretical study of 

the current-voltage characteristics and voltage noise of a semiconductor weak link shunted by a resistor. We calculate the effect of 

the resistor's Johnson thermal noise on the low-frequency voltage noise by performing a stochastic calculus in low frequency. 

We also evaluate the contribution to the noise from the fluctuations in the quasiparticle distribution on the Andreev bound states in the weak link.