Quantifying Trapped Magnetic Vortex Losses in Niobium Resonators at mK Temperatures

Abstract

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$Ω$/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.

Figures (4)

• Figure 1: a) Cartoon schematic of the setup used for our study. The measurement chain includes 46 dB of attenuation, low pass filters (LPF), infrared radiation filters (IRF), a circulator, isolators (Iso) and +35 dB HEMT amplifier. A double layer of mu-metal magnetic shielding was used to minimize the ambient magnetic field within the DR. The Helmholtz coils (HC) are shown in blue. Flux gate (FG) and RuOX temperature (RuOx) sensor positions are also presented. b) A depiction of the 6 GHz cavity with thermal anchoring and the precise location of the Helmholtz coils and diagnostic equipment.
• Figure 2: Quality factor vs on-axis electric field of a 6 GHz cavity measured at temperatures ranging from 0.010 K to 1.289 K after cooling in various applied magnetic fields. Inset shows quality factor measured at an on-axis field of 50 V/m vs temperature. Blue, green, black, and red-hued points correspond to data acquired post cooling in 0 mG, 50 mG, 100 mG, and 250 mG, as described in Table \ref{['tab:magField']}.
• Figure 3: Real part of the sensitivity to trapped magnetic flux as a function of a) field at temperatures of approximately 0.014 K and 1.289 K and b) temperature at 50 V/m post cooling in various magnetic fields. Upper inset plots the imaginary component of the sensitivity to trapped magnetic flux as a function of temperature. Error bars represent the propagated uncertainty arising from data scatter and the applied magnetic field uncertainty. Solid lines in b) represent simultaneous fits to both $S$ and $S'$ for all three data sets using Eq. \ref{['eq:ZT']}. Lower inset compares the cavity angular frequency $\omega$ with the fitted depinning frequency $\omega_d$. Fitting parameters are presented in Table \ref{['tab:fit']}.
• Figure 4: Calculated upper bounds on $T_1$ of a niobium SRF cavity at 6 GHz at 1 V/m considering convolved oxide and vortex contributions (solid red line) and vortex losses in the absence of oxide (blue dashed).