Current dependence of the low bias resistance of small capacitance Josephson junctions

Abstract: The dc current-voltage characteristics of small Josephson junctions reveal features that are not observed in larger junctions, in particular, a switch to the finite voltage state at current values much less than the expected critical current of the junction and a finite resistance in the nominally superconducting regime. Both phenomena are due to the increased sensitivity to noise associated with the small capacitance of the Josephson junction and have been extensively studied a few decades ago. Here I focus on the current bias dependence of the differential resistance of the junction at low current bias in the nominally superconducting regime, using a quantum Langevin equation approach that enables a physically transparent incorporation of the noise environment of the junction. A similar approach might be useful in modeling the sensitivity of superconducting qubits to noise in the microwave regime.