Development of potential-based time domain integral equations for quantum electrodynamics modeling
Roth, Thomas E
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https://hdl.handle.net/2142/109357
Description
Title
Development of potential-based time domain integral equations for quantum electrodynamics modeling
Author(s)
Roth, Thomas E
Issue Date
2020-11-12
Director of Research (if dissertation) or Advisor (if thesis)
Chew, Weng C
Doctoral Committee Chair(s)
Chew, Weng C
Committee Member(s)
Leburton, Jean-Pierre
Popescu, Gabriel
Peng, Zhen
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computational electromagnetics
time domain integral equations
quantum electrodynamics
Abstract
Quantum technologies that significantly depend on electromagnetic effects are becoming of increasing interest to engineers. In many important cases, the quantum electrodynamics models that describe these technologies can be solved using information about the electromagnetic environment provided by computational electromagnetics methods operating purely in the classical regime. However, the unique requirements imposed by these applications are stressing the capabilities of traditional computational electromagnetics methods. To address this, time domain integral equation methods formulated directly in terms of the magnetic vector and electric scalar potentials are systematically developed for the analysis of perfectly conducting and penetrable regions. A rigorous functional framework is utilized to analyze the Sobolev space properties of these integral equations. Discretizations formulated to conform to these Sobolev space properties are shown to be substantially more stable numerically than traditional discretization approaches. These new computational electromagnetics methods are then utilized in a novel framework developed to determine the spatially-dependent quantized field operators produced by a single photon source built from a transmon qubit.
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