Photon-instanton scattering in a superconducting circuit: Beyond the very high impedance regime

TL;DR

This paper develops a numerical scattering theory for instantons in superconducting circuits, extending previous models to better match experimental results across a wider range of impedances without fitting parameters.

Contribution

It introduces a numerical approach to analyze instanton scattering in superconducting circuits, surpassing previous analytical limitations and improving agreement with experiments for lower impedance devices.

Findings

Enhanced theoretical predictions align with experimental data.

Applicable to devices with shorter relaxation times and lower impedances.

Framework useful for broader quantum field theoretical applications.

Abstract

Instantons, semi-classical trajectories of quantum tunneling in imaginary time, have long been used to study thermodynamic and transport properties in a myriad of condensed matter and high energy systems. A recent experiment in superconducting circuits [Phys. Rev. Lett. 126, 197701, (2021)] provided first evidence for direct dynamical signatures of instantons (phase slips), manifested by order-unity inelastic decay probabilities for photons with which they interact, motivating the development of a scattering theory of instantons [Phys. Rev. Lett. 126, 137701, (2021)]. While this framework successfully predicted the measured inelastic decay rates of the photons for several experimental devices, it is valid only if the tunneling time of the instantons is much shorter than the relaxation time due to the environment in which they are embedded, and requires a closed analytical expression for the instanton trajectory. Here, we alleviate these restrictions by incorporating numerical methods that eliminate some of the previously applied approximations. Our results improve the agreement with the experimental measurements, also for devices with lower impedances and thus shorter relaxation times, without fitting parameters. This framework should be useful in many other quantum field theoretical contexts.