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 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.