Linear circuit models for on-chip quantum electrodynamics

TL;DR

This paper introduces linear circuit models for on-chip quantum electrodynamics, enabling simplified analysis of microwave resonator and quantum system interactions with good agreement to experimental data.

Contribution

It develops equivalent circuit models derived from a general Hamiltonian to accurately simulate quantum-electrodynamics interactions using only passive linear elements.

Findings

Circuit models match experimental transmission frequencies

Models accurately predict qubit Lamb shifts

Simplifies understanding of quantum-classical microwave systems

Abstract

We present equivalent circuits that model the interaction of microwave resonators and quantum systems. The circuit models are derived from a general interaction Hamiltonian. Quantitative agreement between the simulated resonator transmission frequency, qubit Lamb shift and experimental data will be shown. We demonstrate that simple circuit models, using only linear passive elements, can be very useful in understanding systems where a small quantum system is coupled to a classical microwave apparatus.