Quantifying Trapped Magnetic Vortex Losses in Niobium Resonators at mK Temperatures

Trapped magnetic vortices in niobium introduce microwave losses that degrade the performance of superconducting resonators. While such losses have been extensively studied above 1~K, we report here their direct quantification in the millikelvin and low-photon regime relevant to quantum devices. Using a high-quality factor 3-D niobium cavity cooled through its superconducting transition in controlled magnetic fields, we isolate vortex-induced losses and find the resistive component of the sensitivity to trapped flux $S$ to be approximately 2~n$\Omega$/mG at 10~mK and 6~GHz. The decay rate is initially dominated by two-level system (TLS) losses from the native niobium pentoxide, with vortex-induced degradation of $T_1$ occurring above $B_{\text{trap}}\sim$~50~mG. In the absence of the oxide, even 10~mG of trapped flux limits performance $Q_0\sim$~10$^{10}$, or $T_1\sim$~350~ms, underscoring the need for stringent magnetic shielding. The resistive sensitivity $S$ decreases with temperature and remains largely field-independent, whereas the reactive component, $S'$, exhibits a maximum near 0.8~K. These behaviors are well modeled within the Coffey-Clem framework in the zero-creep limit, under the assumption that vortex pinning is enhanced by thermally activated processes. Our results suggest that niobium-based transmon qubits can tolerate vortex-induced dissipation at trapped field levels up to several hundred mG, but achieving long coherence times still requires careful magnetic shielding to suppress lower-field losses from other mechanisms.