Investigate material losses in superconducting circuits with multi-mode resonators.*

High Q superconducting cavities are important resources in superconducting quantum circuits. The long-lived bosonic modes in the cavities can be used to store quantum information and enable quantum error correction in a hardware-efficient manner. Improving the coherence of superconducting cavities is crucial to realize practical quantum processors with 3D circuit QED architecture. The coherence of superconducting circuits and superconducting cavities is limited by the losses from their constituent materials. Quantifying the material losses in the devices is crucial to understanding the loss mechanism and improving coherence. In this work, we present a method to quantify material losses using multi-mode superconducting resonators. We apply this technique to measure the material loss properties of aluminum, including the surface resistance, seam conductance, and loss tangent of the surface oxide. Additionally, we use this technique to study the chemical etching process and quantify the improvement on the material losses.  The extracted material losses are valuable information to optimize the circuit designs and fabrication processes. More importantly, correlating the losses with material properties acquired from other material characterization techniques could provide significant insight into the underlying loss mechanism, which is crucial for substantial improvements in material qualities and coherence.