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arXiv:0804.0467 · Applied Physics Letters

A semiempirical model for two-level system noise in superconducting microresonators

Jiansong Gao, M. Daal, John M. Martinis, Anastasios Vayonakis, Jonas Zmuidzinas, B. Sadoulet, Benjamin A. Mazin, Peter K. Day, Henry G. Leduc

Published May 26, 2008• 174 citations
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Abstract

We present measurements of the low-temperature excess frequency noise of four niobium superconducting coplanar waveguide microresonators, with center strip widths sr ranging from 3to20μm. For a fixed internal power, we find that the frequency noise decreases rapidly with increasing center strip width, scaling as 1∕sr1.6. We show that this geometrical scaling is readily explained by a simple semiempirical model which assumes a surface distribution of independent two-level system fluctuators. These results allow the resonator geometry to be optimized for minimum noise.

DOI
10.1063/1.2937855

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We present measurements of the low-temperature excess frequency noise of four niobium superconducting coplanar waveguide microresonators, with center strip widths sr ranging from 3to20μm. For a fixed internal power, we find that the frequency noise decreases rapidly with increasing center strip width, scaling as 1∕sr1.6. We show that this geometrical scaling is readily explained by a simple semiempirical model which assumes a surface distribution of independent two-level system fluctuators. These results allow the resonator geometry to be optimized for minimum noise.
We present measurements of the temperature-dependent frequency shift of five niobium superconducting coplanar waveguide microresonators with center strip widths ranging from 3to50μm, taken at temperatures in the range of 100–800mK, far below the 9.2K transition temperature of niobium. These data agree well with the two-level system (TLS) theory. Fits to this theory provide information on the number of TLSs that interact with each resonator geometry. The geometrical scaling indicates a surface distribution of TLSs and the data are consistent with a TLS surface layer thickness of the order of a few nanometers, as might be expected for a native oxide layer.
We present measurements of the temperature and power dependence of the resonance frequency and frequency noise of superconducting niobium thin-film coplanar waveguide resonators carried out at temperatures well below the superconducting transition (Tc=9.2K). The noise decreases by nearly two orders of magnitude as the temperature is increased from 120to1200mK, while the variation of the resonance frequency with temperature over this range agrees well with the standard two-level system (TLS) model for amorphous dielectrics. These results support the hypothesis that TLSs are responsible for the noise in superconducting microresonators and have important implications for resonator applications such as qubits and photon detectors.
The authors have measured noise in thin-film superconducting coplanar waveguide resonators. This noise appears entirely as phase noise, equivalent to a jitter of the resonance frequency. In contrast, amplitude fluctuations are not observed at the sensitivity of their measurement. The ratio between the noise power in the phase and amplitude directions is large, in excess of 30dB. These results have important implications for resonant readouts of various devices such as detectors, amplifiers, and qubits. They suggest that the phase noise is due to two-level systems in dielectric materials.
Microscopic two-level systems (TLSs) are known to contribute to loss in resonant superconducting microwave circuits. This loss increases at low power and temperatures as the TLSs become unsaturated. We find that the loss is dependent on both the substrate-superconductor interface and the roughness of the surfaces. A native, oxide-free interface reduced the loss due to TLSs. However, a rough surface in the CPW gap did not cause more TLS loss, but the overall loss was significantly increased for the roughest surfaces.
We investigated the loss mechanisms of superconducting circuits with epitaxially grown NbN(100) on MgO(100) substrates by measuring quarter-wave coplanar waveguide resonators with various strip and slot widths. The power dependence of the internal quality factor and the temperature dependence of the resonance frequency shift were evaluated in a dilution refrigerator. The measurement and analysis of the loss in these resonators indicate that the loss was dominated by a two-level system (TLS) loss and the TLS host materials were primarily distributed at the surface of the substrate.
We present measurements of the frequency noise and resonance frequency temperature dependence in planar superconducting resonators on both silicon and sapphire substrates. We show, by covering the resonators with sputtered SiOxlayers of different thicknesses, that the temperature dependence of the resonance frequency scales linearly with thickness, whereas the observed increase in noise is independent of thickness. The frequency noise decreases when increasing the width of the coplanar waveguide in NbTiN on hydrogen passivated silicon devices, most effectively by widening the gap. We find up to an order of magnitude more noise when using sapphire instead of silicon as substrate. The complete set of data points towards the noise being strongly affected by superconductor-dielectric interfaces.