Superconductor-insulator quantum phase transition in a single Josephson junction

The superconductor-to-insulator quantum phase transition in resistively shunted Josephson junctions is investigated by means of path-integral Monte Carlo simulations. Our numerical technique allows to directly access the regime of the Josephson-to-charging energy ratios $E_J{/E}_C$ of order one. Our results unambiguously support an earlier theoretical conjecture, based on renormalization-group calculations, that at $\overrightarrow{T}0$ the dissipative phase transition occurs at a universal value of the shunt resistance $R_S{=h/4e}^2$ for all values $E_J{/E}_C.$ On the other hand, finite-temperature effects are shown to turn this phase transition into a crossover, whose position depends significantly on $E_J{/E}_C,$ as well as on the dissipation strength and temperature. The latter effect needs to be taken into account in order to reconcile earlier theoretical predictions with recent experimental results.