Consistent Quantization of Nearly Singular Superconducting Circuits

Physical Review X, vol. 13

Abstract

The 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.

Authors 2

1. Martin Rymarz Aachen JARA-Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   JARA-Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

2. David Peter Divincenzo Aachen JARA-Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   JARA-Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

   Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52425 Jülich, Germany