Frequency-dependent admittance of a short superconducting weak link

Abstract

We consider the linear and nonlinear electromagnetic responses of a nanowire connecting two bulk superconductors. The Andreev states appearing at a finite phase bias substantially affect the finite-frequency admittance of such a wire junction. Electron transitions involving the Andreev levels are easily saturated, leading to the nonlinear effects in photon absorption for the subgap photon energies. We evaluate the complex admittance analytically at an arbitrary frequency and arbitrary, possibly nonequilibrium, occupation of the Andreev levels. Special care is given to the limits of a single-channel contact and a disordered metallic weak link. We also evaluate the quasistatic fluctuations of admittance induced by fluctuations of the occupation factors of the 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 quasistatic 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.