Capacitors with very low loss: Cryogenic vacuum-gap capacitors

We report on measurements of capacitors with about 1 pF of capacitance, which have unmeasurably small leakage at very low frequencies, placing a lower bound of about 10(19)Omega on the parallel resistance at an effective frequency of 1 mHz, These measurements are made possible by two themes: the use of vacuum-gap capacitors (i.e., no dielectric material, operated in vacuum), and detection of leakage using single electron tunneling (SET) electrometers, which have very high input impedance, We also report on good achieved results in time stability and lack of frequency and voltage dependence.