Quantum charge diffusion in underdamped Josephson junctions and superconducting nanowires

The effect of quantum fluctuations on the current-voltage characteristics of Josephson junctions and superconducting nanowires is studied in the underdamped limit. Quantum fluctuations induce transitions between a Coulomb–blockade and a supercurrent branch, and can significantly modify the shape of current-voltage characteristics in the case of a highly resistive environment. Owing to the phase-charge duality, our results can be directly extended to the opposite overdamped limit. Introduction. – A small-capacitance Josephson junction is a quantum system with rich dynamics. The two conjugate variables are the superconducting phase difference φ across the junction and the charge Q on its electrodes. Correspondingly, at low temperatures the behavior of the junction is determined by the competition between the Josephson energy EJ and the charging energy EC = (2e) /2C, where C is the junction capacitance [1]. If EJ ≫ EC , φ is well-defined and a phase-coherent Cooperpair current can flow through the junction in the absence of an external voltage V . In the opposite limit EJ ≪ EC an insulating state with a well-defined charge Q on the electrodes is possible. At the same time, the dynamics of φ and Q is crucially influenced by dissipation caused by the electromagnetic environment surrounding the junction. Because of the mutual interplay of quantum mechanics, nonlinearity and dissipation, the consistent theoretical description of Josephson junctions still remains far from being complete. The dc current-voltage (I-V ) characteristics of a Josephson junction embedded in a circuit of resistance R have been well studied in the so-called overdamped [1] case corresponding to small values of R/RQ (RQ = h/4e 2 is the resistance quantum) and the ratio EJ/EC [2–8]. For small R < RQ, the supercurrent peak at zero voltage acquires a finite width. With increasing R, quantum fluctuations of the phase become more important and the supercurrent peak gradually moves to higher voltages. This corresponds to the transition (driven by the environment) from superconducting behavior found for small R to a complete Coulomb blockade when R > RQ. Meanwhile, the opposite underdamped regime, which has been extremely difficult to achieve experimentally, has attracted less attention. However, recently experiments were performed [9, 10] on junctions with EJ/EC > 1, embedded in a tunable, highly resistive environment, R ≫ RQ, enabling the study of the same junction in different environments. In particular, a voltage peak near zero current followed by a back-bending to lower voltages at higher currents was observed. This is the so-called Bloch nose [11] which, in accordance with a duality property [4,12–14], resembles the I-V characteristic of an overdamped junction but with the role of voltage and current interchanged. A quantitative comparison between theory and experiment has been made in the classical limit where thermal fluctuations dominate [10, 15]. In this Letter we study for the first time the influence of quantum fluctuations on the I-V characteristics of an underdamped Josephson junction. We show that the quantum-mechanical nature of the electromagnetic environment can strongly modify the crossover from Coulomb blockade to superconducting behavior. Without fluctuations the I-V characteristic contains a sharp cusp that connects two distinct branches: a zero–current finite–voltage branch corresponding to Coulomb blockade and a supercurrent branch corresponding to Bloch oscillations of the