The microwave performance of amorphous dielectric materials at very low temperatures and very low excitation strengths displays significant excess loss. Here, we present the loss tangents of some common amorphous and crystalline dielectrics, measured at low temperatures (T<100 mK) with near single-photon excitation energies, E ω0 ∼1, using both coplanar waveguide and lumped LC resonators. The loss can be understood using a two-level state defect model. A circuit analysis of the half-wavelength resonators we used is outlined, and the energy dissipation of such a resonator on a multilayered dielectric substrate is theoretically considered.
Bibliographical noteFunding Information:
Devices were made at the UCSB and Cornell Nanofabrication Facilities, a part of the NSF-funded National Nanotechnology Infrastructure Network. This work was supported by ARDA under Grant No. W911NF-04-1-0204 and by the NSF under Grant No. CCF-0507227.