Introduction to Quantum Electromagnetic Circuits

TL;DR

This paper reviews the quantum treatment of electromagnetic circuits, focusing on Hamiltonian construction, quantization including dissipation, and the role of Josephson elements and superconducting artificial atoms.

Contribution

It provides an updated, modernized overview of quantum electromagnetic circuits, emphasizing Hamiltonian formulation, dissipation quantization, and superconducting circuit components.

Findings

Hamiltonian construction for general circuits including dissipation

Quantum treatment of dissipation in circuits

Overview of superconducting artificial atoms

Abstract

The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture notes, has 3 main parts. The first part describes how to construct a Hamiltonian for a general circuit, which can include dissipative elements. The second part describes the quantization of the circuit, with an emphasis on the quantum treatment of dissipation. The final part focuses on the Josephson non-linear element and the main linear building blocks from which superconducting circuits are assembled. It also includes a brief review of the main types of superconducting artificial atoms, elementary multi-level quantum systems made from basic circuit elements.