Voltage noise, switching rates, and multiple phase-slips in moderately damped Josephson junctions

We study the voltage noise properties including the switching rates and statistics of phase-slips in moderately damped Josephson junctions using a novel efficient numerical approach combining the matrix continued-fraction method with the full counting statistics. By analyzing the noise results obtained for the RCSJ model we identify different dominating components, namely the thermal noise close to equilibrium (small current-bias regime), the shot noise of (multiple) phase-slips in the intermediate range of biases and the switching noise for yet higher bias currents. We extract thus far inaccessible characteristic rates of phase-slips in the shot noise regime as well as the escape and retrapping rates in the switching regime as functions of various junction's parameters. The method can be extended and applied to other experimentally relevant Josephson junction circuits.Comment: 5 pages, 4 figures of the main text + 7 pages of supplemen

Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0−π0-\pi transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetrically attached to superconducting leads is studied via the perturbation expansion in the interaction strength. We find the exact asymptotic form of the spin-symmetric solution for the Andreev states continuously approaching the Fermi level. We thereby derive a critical interaction at which the Andreev states at zero temperature merge at the Fermi energy, being the upper bound for the $0-\pi$ transition. We show that the spin-symmetric solution becomes degenerate beyond this interaction, in the $\pi$ phase, and the Andreev states do not split unless the degeneracy is lifted. We further demonstrate that the degeneracy of the spin-symmetric state extends also into the $0$ phase in which the solutions with zero and non-zero frequencies of the Andreev states may coexist.Comment: 12 pages, 4 figure

Effective low-energy models for superconducting impurity systems

We present two complementary methods to calculate the Andreev bound state energies of a single-level quantum dot connected to superconducting leads described by the superconducting impurity Anderson model. The first method, which is based on a mapping to a low-energy model, can be utilized to extract the Andreev bound state energies from finite-temperature, imaginary-time quantum Monte Carlo data without the necessity of any analytic continuation technique. The second method maps the full model on an exactly solvable superconducting atomic limit with renormalized parameters. As such, it represents a fast and reliable method for a quick scan of the parameter space. We demonstrate that after adding a simple band correction this method can provide predictions for measurable quantities, including the Josephson current, that are in a solid quantitative agreement with precise results obtained by the numerical renormalization group and quantum Monte Carlo.Comment: 16 pages, 7 figure