Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics

Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics

Gely, M.F. (TU Delft QN/Steele Lab)
Parra-Rodriguez, Adrian (University of the Basque Country)
Bothner, D. (TU Delft QN/Steele Lab)
Blanter, Y.M. (TU Delft QN/Blanter Group)
Bosman, S.J. (TU Delft QN/Steele Lab)
Solano, Enrique (University of the Basque Country; Basque Foundation for Science)
Steele, G.A. (TU Delft QN/Steele Lab)

2017-06-14

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.

http://resolver.tudelft.nl/uuid:bb31e230-9575-42f2-b564-0c018011ca61

https://doi.org/10.1103/PhysRevB.95.245115

1098-0121

Physical Review B (Condensed Matter and Materials Physics), 95 (24)

Institutional Repository

journal article

© 2017 M.F. Gely, Adrian Parra-Rodriguez, D. Bothner, Y.M. Blanter, S.J. Bosman, Enrique Solano, G.A. Steele