Three-dimensional superconducting resonators at $T < 20$ mK with the photon lifetime up to $τ=2$ seconds

Abstract: Very high quality factor superconducting radio frequency cavities developed for accelerators can enable fundamental physics searches with orders of magnitude higher sensitivity, as well as offer a path to a 1000-fold increase in the achievable coherence times for cavity-stored quantum states in the 3D circuit QED architecture. Here we report the first measurements of multiple accelerator cavities of $f_0=$1.3, 2.6, 5 GHz resonant frequencies down to temperatures of about 10~mK and field levels down to a few photons, which reveal record high photon lifetimes up to 2 seconds, while also further exposing the role of the two level systems (TLS) in the niobium oxide. We also demonstrate how the TLS contribution can be greatly suppressed by the vacuum heat treatments at 340-450$^\circ$C.