# Phase Slips in Superconducting Weak Links

## TL;DR

This paper investigates the nonlinear dynamics of phase slips in superconducting weak links, revealing that their onset occurs through an infinite period bifurcation, with analytical and numerical results aligning well.

## Contribution

It introduces a weakly nonlinear approximation for phase slips in weak links and identifies the bifurcation mechanism behind their onset, which was previously not well understood.

## Key findings

- Phase slips occur via an infinite period bifurcation.
- The voltage-current dependence shows characteristic signatures of this bifurcation.
- Analytical results agree with numerical simulations.

## Abstract

Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly non-linear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires and slabs. Using the numerical solution of the time-dependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.