Jaynes Cummings treatment of superconducting resonators with dielectric loss due to two-level systems

TL;DR

This paper provides a quantum mechanical analysis of dielectric loss in superconducting resonators caused by two-level systems, revealing differences from classical models especially in strong coupling regimes.

Contribution

It introduces a quantum Jaynes-Cummings model to analyze dielectric loss, distinguishing strong and weak coupling regimes and saturation effects.

Findings

Quantum theory aligns with classical in weak coupling.

Quantum predicts lower loss in strong coupling unsaturated regime.

Saturation photon number is coupling-independent in quantum model.

Abstract

We perform a quantum mechanical analysis of superconducting resonators subject to dielectric loss arising from charged two-level systems. We present numerical and analytical descriptions of the dynamics of energy decay from the resonator within the Jaynes-Cummings model. Our analysis allows us to distinguish the strong and weak coupling regimes of the model and to describe within each regime cases where the two-level system is unsaturated or saturated. We find that the quantum theory agrees with the classical model for weak coupling. However, for strong coupling the quantum theory predicts lower loss than the classical theory in the unsaturated regime. Also, in contrast to the classical theory, the photon number at which saturation occurs in the strong coupling quantum theory is independent of the coupling between the resonator and the two-level system.