Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics

Mario F. Gely, Adrian Parra-Rodriguez, Daniel Bothner, Ya M. Blanter, Sal J. Bosman, Enrique Solano, Gary A. Steele

Research output: Contribution to journalArticleScientificpeer-review

27 Citations (Scopus)
53 Downloads (Pure)


Circuit quantum electrodynamics (QED) studies the interaction of artificial atoms, open transmission lines, and electromagnetic resonators fabricated from superconducting electronics. While the theory of an artificial atom coupled to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a first-principles model of a multimode resonator coupled to a Josephson junction atom. Studying the model in the absence of any cutoff, in which the coupling rate to mode number n scales as n for n up to, we find that quantities such as the Lamb shift do not diverge due to a natural rescaling of the bare atomic parameters that arises directly from the circuit analysis. Introducing a cutoff in the coupling from a nonzero capacitance of the Josephson junction, we provide a physical interpretation of the decoupling of higher modes in the context of circuit analysis. In addition to explaining the convergence of the quantum Rabi model with no cutoff, our work also provides a useful framework for analyzing the ultrastrong coupling regime of a multimode circuit QED.

Original languageEnglish
Article number245115
Number of pages5
JournalPhysical Review B (Condensed Matter and Materials Physics)
Issue number24
Publication statusPublished - 14 Jun 2017

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