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001007153 1001_ $$0P:(DE-HGF)0$$aRymarz, Martin$$b0$$eCorresponding author
001007153 245__ $$aConsistent Quantization of Nearly Singular Superconducting Circuits
001007153 260__ $$aCollege Park, Md.$$bAPS$$c2023
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001007153 520__ $$aThe theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian describing these circuits. In many simplified versions of these networks, the modeling involves a singular Lagrangian that employs Kirchhoff’s laws to eliminate inherent constraints of the system. In this work, we demonstrate the failure of such singular theories for the quantization of realistic, nearly singular superconducting circuits. Instead, we rigorously prove the validity of a perturbative analysis within the Born-Oppenheimer approximation. In particular, we find that the limiting behavior of the low-energy dynamics obtained from the regularized approach exhibits a fixed-point structure flowing to one of a few universal fixed points as parasitic capacitance values go to zero. This singular limit of the regularized analysis is, in many cases, completely unlike the singular theory. Consequently, we conclude that classical network synthesis techniques which build on Kirchhoff’s laws must be critically examined prior to applying circuit quantization.
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001007153 536__ $$0G:(GEPRIS)390534769$$aDFG project 390534769 - EXC 2004: Materie und Licht für Quanteninformation (ML4Q) (390534769)$$c390534769$$x1
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001007153 7001_ $$0P:(DE-Juel1)143759$$aDiVincenzo, David P.$$b1
001007153 773__ $$0PERI:(DE-600)2622565-7$$a10.1103/PhysRevX.13.021017$$gVol. 13, no. 2, p. 021017$$n2$$p021017$$tPhysical review / X$$v13$$x2160-3308$$y2023
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