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arXiv:0802.4457 · Applied Physics Letters

Experimental evidence for a surface distribution of two-level systems in superconducting lithographed microwave resonators

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

Published Apr 14, 2008• 389 citations
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Abstract

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.

DOI
10.1063/1.2906373

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Chinese Physics Letters•Jun 1, 2014•2 citations
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.
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.
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.
High quality factor, i.e. low loss, microwave resonators are important for quantum information storage and addressing. In this work we study the resonance frequency and loss in superconducting coplanar waveguide resonators as a function of power and temperature. We find that there is increased loss at low power and low temperature. The increased loss is attributed to the existence of two-level systems (TLS) at the surfaces, interfaces, and in the bulk of insulators deposited on the structures. We show that both the temperature dependence of the resonant frequency and the power dependence of the loss can be used to find the TLS contribution to the loss. The TLS intrinsic loss tangent derived from the frequency shift data at high power is shown to agree well with the direct loss measurement at low power. The former allows for a relatively fast measurement of the TLS loss. As an example, we measure the properties of amorphous AlOXdeposited on the resonators and find a TLS loss tangent of 1 × 10-3.
The high critical magnetic field and relatively high critical temperature of niobium nitride (NbN) make it a promising material for applications in superconducting quantum technology. However, NbN-based superconducting circuits are sensitive to decoherence sources such as two-level system (TLS) defects. Here, we numerically and experimentally investigate NbN superconducting microwave coplanar waveguide resonator arrays with a 100 nm thickness, capacitively coupled to a common coplanar waveguide on a silicon chip. We observe that the resonators' internal quality factor (QiQ_{i}Qi​) decreases fromQi∼1.07×106Q_{i}\sim 1.07\times 10^{6}Qi​∼1.07×106in a high power regime toQi∼1.36×105Q_{i}\sim 1.36\times 10^{5}Qi​∼1.36×105in the single photon regime. Data from this study is consistent with the TLS theory, which describes the TLS interactions in resonator substrates and interfaces. Moreover, we study the temperature (TTT) dependence ofQiQ_{i}Qi​and resonance frequencyfrf_{r}fr​of coplanar waveguide resonators to characterize the quasiparticle density. We observe that the increase in kinetic inductance at higher temperatures is the main reason for the frequency shift. Finally, we measurefrf_{r}fr​andQiQ_{i}Qi​in response to in-plane magnetic fields (B∣∣B_{||}B∣∣​). We verify thatQiQ_{i}Qi​stays well above10410^{4}104up toB∣∣B_{||}B∣∣​= 240 mT in the photon number< ⁣nph ⁣>< \! n_{ph} \! ><nph​>= 1.8 atTTT= 100 mK. Our results could enable the development of robust microwave superconducting circuits for circuit quantum electrodynamics at high magnetic fields required for hybrid superconducting-semiconducting quantum circuits.
We present the measurements of the temperature dependence of the internal quality factor ( Q i ) of a microwave resonator, well below the superconducting transition temperature. The device is a quarter-wavelength niobium ( T c = 9.2 K) coplanar waveguide resonator. The measured | S 21 | parameter shows typically the skewed Lorentzian distributions, from which the fitted quality factor monotonically decreases with the temperature increasing from 30 mK to 900 mK. It is observed that for the lower temperature range (i.e., at T < 700 mK) the temperature dependence of the fitted Q i deviates significantly from the predictions of the usual Mattis—Bardeen theory. The measured 3 dB internal quality factor Q ′ i also verifies such an anomalous temperature dependence. Physically, this phenomenon could be attributed dominantly to the effects of the two-level systems in the device, rather than the usual temperature-dependent complex conductance.