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Circuit QED spectra in the ultrastrong coupling regime: How they differ from cavity QED

Samuel Napoli1,*, Alberto Mercurio1,2,3,†, Daniele Lamberto1, Andrea Zappalà1, Omar Di Stefano1, and Salvatore Savasta1

  • 1Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, I-98166 Messina, Italy
  • 2Laboratory of Theoretical Physics of Nanosystems (LTPN), Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
  • 3Center for Quantum Science and Engineering, EPFL, CH-1015 Lausanne, Switzerland

  • *Contact author: samuel.napoli@studenti.unime.it
  • †Contact author: alberto.mercurio96@gmail.com
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Phys. Rev. Research 7, 033037 – Published 8 July, 2025

DOI: https://doi.org/10.1103/9zl7-31f3

Abstract

Cavity quantum electrodynamics (QED) investigates the interaction between resonator-confined radiation and natural atoms. Similar phenomena can be explored using superconducting artificial atoms coupled to microwave resonators. Here, we examine incoherent and coherent spectra in a circuit QED system consisting of a flux qubit coupled to an LC resonator, considering different coupling configurations to the output transmission line. Although such systems can be effectively described by the quantum Rabi model, we demonstrate that the choice of the coupling between the resonator and the input-output channel can significantly affect the emission properties, particularly in the ultrastrong coupling regime. Specifically, we show that when the resonator is capacitively coupled with the input-output transmission line, the spectral features at zero flux offset can be mapped onto those of the cavity QED model. However, this correspondence breaks down for the mutual inductive coupling case. Extending our analysis to the parity-symmetry broken regime of the flux qubit, we further highlight how capacitive and inductive coupling mechanisms lead to distinct spectral features, emphasizing the necessity of a careful input-output treatment for an accurate description of the emission processes.

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Phys. Rev. Research 7, 033037– Published 8 July, 2025
  • Received 3 October 2024
  • Accepted 23 May 2025
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