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Three-dimensional microwave waveguide cavities are essential tools for manycavity quantum electrodynamics experiments. However, the need to controlquantum emitters with dc magnetic fields inside the cavity often limits suchexperiments to normal-conducting cavities with relatively low quality factorsof about $10^4$. Similarly, controlling quantum emitters with dc electricfields in normal- and superconducting waveguide cavities has so far beendifficult, because the insertion of dc electrodes has strongly limited thequality factor. Here, we present a method to apply dc electric fields within asuperconducting waveguide cavity, which is based on the insertion of dcelectrodes at the nodes of the microwave electric field. Moreover, we present amethod to apply dc magnetic fields within the same cavity by trapping themagnetic flux in holes positioned in facing walls of the cavity. We demonstratethat the $\text{TE}_{301}$ mode of such a superconducting, rectangular cavitymade from niobium maintains a high internal quality factor of $Q_{\text{int}}\sim 1.7 \cdot 10^6$ at the few photon level and a base temperature of$3~\text{K}$. A cloud of Rydberg atoms coupled to the microwave electric fieldof the cavity is used to probe the applied dc electric and magnetic fields viathe quadratic Stark effect and the Zeeman effect, respectively.

Applying Electric and Magnetic Field Bias in a 3D Superconducting Waveguide Cavity with High Quality Factor