Quantum-Noise Theory for the Resistively Shunted Josephson Junction

Abstract

It is shown that the low-frequency spectral density of the voltage noise in a current-biased Josephson junction with critical current ${I}_{0}$, shunt resistance $R$, and small capacitance is $\frac{e{{I}_{0}}^{2}{R}^{3}}{\ensuremath{\pi}V}$ in the limit $\mathrm{eV}\ensuremath{\gg}{k}_{\mathrm{B}}T{(\frac{I}{{I}_{0}})}^{2}$ and $I>{I}_{0}$, where $V$ is the voltage and $I$ is the current. The noise arises from zero-point current fluctuations in the shunt resistor. The rounding of the current-voltage characteristic caused by the quantum fluctuations and the effects of nonzero junction capacitance are calculated.