Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime

TL;DR

This paper explores the spectral characteristics of circuit-QED systems across a range of coupling regimes, revealing multiple spectral transformations and their relation to energy level crossings and symmetries.

Contribution

It identifies and characterizes the spectral features of circuit-QED systems in the intermediate coupling regime between ultrastrong and deep-strong, expanding understanding of spectral evolution.

Findings

Spectral features change qualitatively with increasing coupling strength.

Multiple coupling regimes with distinct spectral signatures are identified.

Spectral transformations relate to energy level crossings and symmetry changes.

Abstract

We report on spectra of circuit-quantum-electrodynamics (QED) systems in an intermediate regime that lies between the ultrastrong and deep-strong-coupling regimes, which have been reported previously in the literature. Our experimental results, along with numerical simulations, demonstrate that as the coupling strength increases, the spectrum of a circuit-QED system undergoes multiple qualitative transformations, such that several coupling regimes are identified, each with its own unique spectral features. The different spectral transformations can be related to crossings between energy level differences and to changes in the symmetries of the energy eigenstates. These results allow us to use qualitative spectral features to infer certain properties and parameters of the system.