Frequency-dependent admittance of a short superconducting weak link

TL;DR

This paper analyzes the frequency-dependent admittance of superconducting nanowire weak links, highlighting nonlinear effects, fluctuations, and implications for qubit applications, with analytical evaluation across various regimes.

Contribution

It provides an analytical framework for the admittance of superconducting weak links considering non-linearities, fluctuations, and non-equilibrium conditions, comparing them to tunnel junctions.

Findings

Andreev states significantly influence admittance.

Nonlinear effects arise from saturation of Andreev level transitions.

Fluctuations in inductance are larger in weak links than tunnel junctions.

Abstract

We consider the linear and non-linear electromagnetic responses of a nanowire connecting two bulk superconductors. Andreev states appearing at a finite phase bias substantially affect the finite-frequency admittance of such a wire junction. Electron transitions involving Andreev levels are easily saturated, leading to the nonlinear effects in photon absorption for the sub-gap photon energies. We evaluate the complex admittance analytically at arbitrary frequency and arbitrary, possibly non-equilibrium, occupation of Andreev levels. Special care is given to the limits of a single-channel contact and a disordered metallic weak link. We also evaluate the quasi-static fluctuations of admittance induced by fluctuations of the occupation factors of Andreev levels. In view of possible qubit applications, we compare properties of a weak link with those of a tunnel Josephson junction. Compared to the latter, a weak link has smaller low-frequency dissipation. However, because of the deeper Andreev levels, the low-temperature quasi-static fluctuations of the inductance of a weak link are exponentially larger than of a tunnel junction. These fluctuations limit the applicability of nanowire junctions in superconducting qubits.