Nonequilibrium quasiparticle distribution in superconducting resonators: analytical approach

TL;DR

This paper derives analytical solutions for nonequilibrium quasiparticle distributions in superconducting resonators and examines their effects on resonator properties, highlighting the significance of nonequilibrium phenomena at different temperatures.

Contribution

The paper provides the first approximate analytical approach to model nonequilibrium quasiparticle distributions in superconducting resonators.

Findings

Nonequilibrium effects are evident at intermediate temperatures due to photon heating.

Low-temperature data cannot be explained by photon-induced heating.

Analytical solutions help interpret experimental measurements of resonator quality and frequency.

Abstract

In the superconducting state, the presence of a finite gap in the excitation spectrum implies that the number of excitations (quasiparticles) is exponentially small at temperatures well below the critical one. Conversely, minute perturbations can significantly impact both the distribution in energy and number of quasiparticles. Typically, the interaction with the electromagnetic environment is the main perturbation source driving quasiparticles out of thermal equilibrium, while a phonon bath is responsible for restoration of equilibrium. Here we derive approximate analytical solutions for the quasiparticle distribution function in superconducting resonators and explore the impact of nonequilibrium on two measurable quantities: the resonator's quality factor and its resonant frequency. Applying our results to experimental data, we conclude that while at intermediate temperatures there is clear evidence for the nonequilibrium effects due to heating of the quasiparticles by photons, the low-temperature measurements are not explained by this mechanism.