Three-Dimensional Superconducting Resonators at $T<20$ mK with Photon Lifetimes up to $\tau =2$ s

Very-high-quality-factor superconducting radio-frequency cavities developed for accelerators can enable fundamental physics searches with orders of magnitude higher sensitivity, and they can also offer a path to a 1000-fold increase in the achievable coherence times for cavity-stored quantum states in three-dimensional circuit QED architecture. Here we report measurements of multiple accelerator cavities of resonant frequencies of $f_0=1.3$, 2.6, 5 GHz down to temperatures of about 10 mK and field levels down to a few photons, which reveal very long photon lifetimes up to 2 s, while also further exposing the role of the two-level systems (TLS) in niobium oxide. We also demonstrate how the TLS contribution can be greatly suppressed by vacuum heat treatments at 340–450 ${}^{\circ }\mathrm{C}$.

Figure 1

(a) Single-cell cavities of the TESLA geometry used for the measurements. (b) Distributions of the magnetic and electric fields in the TM010 mode (half of the rotationally symmetric cavity is shown); the coupling to the mode is performed using pin couplers on the cavity axis on both sides. (c) The typical microwave setup used for measurements (the attenuators and the amplifiers are different in some cases for different frequencies and cooldown cycles).

Figure 2

Intrinsic cavity quality factors of the investigated 1.3-, 2.6-, and 5-GHz cavities as a function of the accelerating field at temperatures $1.4<T<1.5$ K.

Figure 3

Average photon population decay upon switching the rf power off measured in the 5-GHz cavities before and after heat treatment at ${450}^{\circ }\mathrm{C}$. Blue and black curves correspond to the decays from different starting fields and with different filtering bandwidths (100 Hz and 10 Hz, respectively). The red lines show linear fits for both. The magenta and dark yellow lines show stored energy decays of the ${450}^{\circ }\mathrm{C}$ treated cavity with the much longer photon lifetime.

Figure 4

Intrinsic cavity quality factor $Q$ of the 1.3-, 2.6-, and 5-GHz cavities as a function of temperature. Previously, SRF cavities have been studied at temperatures above about 1.3 K. Below about 1 K a significant decrease in $Q$ is observed consistent with the TLS dissipation; the red lines show TLS model fits. A dramatic increase in $Q$ associated with the oxide-modifying heat treatment is apparent on the 1.3-GHz and 5-GHz cavities.

Figure 5

TOF-SIMS depth profiles obtained on the cavity cutout revealing the changes in the niobium pentoxide and nitrogen-related signals after ${400}^{\circ }\mathrm{C}$ in situ heat treatment. About a 5-nm-thick ${\mathrm{Nb}}_2{\mathrm{O}}_5$ pentoxide layer is completely dissolved after the ${400}^{\circ }\mathrm{C}$ treatment. Another apparent change is the increase in the nitrogen level within approximately 10 nm of the surface.