Single crystal silicon capacitors with low microwave loss in the single photon regime

We have fabricated superconducting microwave resonators in a lumped element geometry using single crystal silicon dielectric parallel plate capacitors with C>2 pF. Aluminum devices with resonant frequencies between 4.0 and 6.5 GHz exhibited an average internal quality factor Q_i of 2× 10 ⁵ in the single photon excitation regime at T=20 mK. Attributing the observed loss solely to the capacitive element, our measurements place an upper bound on the loss tangent of the silicon dielectric layer of tan δ_i =5× 10^-6. This level of loss is an order of magnitude lower than is currently observed in structures incorporating amorphous dielectric materials, thus making single crystal silicon capacitors an attractive, robust route for realizing long-lived quantum circuits.