M ay 2 01 0 Minimal resonator loss for circuit quantum electrodynamics

In circuit quantum electrodynamics quantum information processing is done by coupling the qubit state to a single photon bound to a superconducting resonator [1]. The lifetime of a single photon with frequency f is defined by: τ = Q/2πf [2], therefore a high resonator quality factor (Q) is needed to maximize the lifetime. Presently used resonators, made from Nb or Al, have quality factors on the order of 10 to 10 [2–6]. In contrast, superconducting resonators for astronomical photon detection [7] have shown quality factors in excess of a million. However, these quality factors are measured in the many-photon regime. One would like to maintain these high values down to the single photon level. Therefore, we study the unloaded quality factor of NbTiN and, for comparison, Ta quarterwave resonators down to the single photon level. NbTiN has been shown to follow Mattis-Bardeen theory more closely than Nb, Al or Ta, indicating it has a minimal dielectric layer compared to the latter materials [8]. We find that in the single photon regime the quality factor of NbTiN resonators is so high that the loss is largely due to the exposed substrate surface. In contrast, for Ta resonators the quality factor is limited by the metal surface. We show that a further reduction of the loss in NbTiN resonators is achieved by removing the substrate from the regions with a high electric field density. This increases the quality factor to half a million for resonators with a central line width of 6 μm, three times higher than recently reported for Re [2].