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

Three-dimensional microwave waveguide cavities are essential tools for many cavity quantum electrodynamics experiments. However, the need to control quantum emitters with dc magnetic fields inside the cavity often limits such experiments to normal-conducting cavities with relatively low quality factors of about $10^4$. Similarly, controlling quantum emitters with dc electric fields in normal- and superconducting waveguide cavities has so far been difficult, because the insertion of dc electrodes has strongly limited the quality factor. Here, we present a method to apply dc electric fields within a superconducting waveguide cavity, which is based on the insertion of dc electrodes at the nodes of the microwave electric field. Moreover, we present a method to apply dc magnetic fields within the same cavity by trapping the magnetic flux in holes positioned in facing walls of the cavity. We demonstrate that the $\text{TE}_{301}$ mode of such a superconducting, rectangular cavity made 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 field of the cavity is used to probe the applied dc electric and magnetic fields via the quadratic Stark effect and the Zeeman effect, respectively.