In-situ Characterization of Light-Matter Coupling in Multimode Circuit-QED Systems

TL;DR

This paper introduces a versatile measurement protocol for characterizing light-matter interactions in complex multimode cavity-QED systems, using AC-Stark and Kerr effects without requiring single-photon resolution.

Contribution

The authors develop a general, calibration-free method to determine mode-specific light-matter couplings in multimode cavity-QED systems, validated on a superconducting circuit.

Findings

Successfully measured coupling constants for multiple modes

Validated the method across different detunings and photon modes

Demonstrated consistency of coupling measurements using Kerr effects

Abstract

Multimode cavity-QED systems can be leveraged to explore a wide range of physical phenomena; however, a complex multimode environment makes systematic characterization of light-matter interactions challenging. Here we present a general measurement protocol, applicable to both atomic and synthetic cavity-QED systems, that enables the determination of coupling to individual photonic modes. The method leverages measurements of the AC-Stark and Kerr effects, along with known detuning dependencies, to eliminate the need for single-photon resolution, independent photon-number calibration, or insertion-loss calibration. We demonstrate the method using a superconducting transmon qubit coupled to a one-dimensional microwave resonator lattice. We validate the consistency of the extracted light-matter couplings $g$ determined at multiple qubit detunings, and from the self-Kerr and cross-Kerr shifts for three photon modes, which provide separate measurements of $g$ for each of the three modes.