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arXiv:2402.10775 · Physical Review Applied

Intermodulation spectroscopy and the nonlinear response of two-level systems in superconducting coplanar-waveguide resonators

Janka Biznárová, J. C. Rivera Hernández, Daniel Forchheimer, Jonas Bylander, David B. Haviland, Gustav Andersson

Published Jul 24, 2024• 2 citations
arXivHTMLPDF

Abstract

Two-level system (TLS) loss typically limits the coherence of superconducting quantum circuits. The loss induced by TLS defects is nonlinear, resulting in quality factors with a strong dependence on the circulating microwave power. We observe frequency mixing due to this nonlinearity by applying a two-tone drive to a coplanar waveguide resonator and measuring the intermodulation products using a multifrequency lock-in technique. This intermodulation spectroscopy method provides an efficient approach to characterizing TLS loss in superconducting circuits. Using harmonic balance reconstruction, we recover the nonlinear parameters of the device-TLS interaction, which are in good agreement with the standard tunneling model for TLSs. Published by the American Physical Society 2024

DOI
10.1103/physrevapplied.22.014063

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Two-level system (TLS) loss typically limits the coherence of superconducting quantum circuits. The loss induced by TLS defects is nonlinear, resulting in quality factors with a strong dependence on the circulating microwave power. We observe frequency mixing due to this nonlinearity by applying a two-tone drive to a coplanar waveguide resonator and measuring the intermodulation products using a multifrequency lock-in technique. This intermodulation spectroscopy method provides an efficient approach to characterizing TLS loss in superconducting circuits. Using harmonic balance reconstruction, we recover the nonlinear parameters of the device-TLS interaction, which are in good agreement with the standard tunneling model for TLSs. Published by the American Physical Society 2024
Atomic sized two-level systems (TLSs) in amorphous dielectrics are known as a major source of loss in superconducting devices. In addition, individual TLSs are known to induce large frequency shifts due to strong coupling to the devices. However, in the presence of a broad ensemble of TLSs these shifts are symmetrically canceled out and not observed in a typical single-tone spectroscopy experiment. We introduce a two-tone spectroscopy on the normal modes of a pair of coupled superconducting coplanar waveguide resonators to reveal this effect. Together with an appropriate saturation model this enables us to extract the average single-photon Rabi frequency of dominant TLSs to be ${\mathrm{\ensuremath{\Omega}}}_{0}/2\ensuremath{\pi}\ensuremath{\approx}79$ kHz. At high photon numbers we observe an enhanced frequency shift due to nonlinear kinetic inductance when using the two-tone method and estimate the value of the nonlinear coefficient as $K/2\ensuremath{\pi}\ensuremath{\approx}\ensuremath{-}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ Hz/photon. Furthermore, the lifetime of each resonance can be controlled (increased) by pumping of the other mode as demonstrated both experimentally and theoretically.
© 2019 American Physical Society. Superconducting quantum-computing architectures comprise resonators and qubits that experience energy loss due to two-level systems (TLSs) in bulk and interfacial dielectrics. An understanding of these losses is critical to improving performance in superconducting circuits. In this work, we present a method for quantifying the TLS losses of different bulk and interfacial dielectrics present in superconducting coplanar-waveguide (CPW) resonators. By combining statistical characterization of sets of specifically designed CPW resonators on isotropically etched silicon substrates with detailed electromagnetic modeling, we determine the separate loss contributions from individual material interfaces and bulk dielectrics. This technique for analyzing interfacial TLS losses can be used to guide targeted improvements to qubits, resonators, and their superconducting fabrication processes.
So-called two-level system (TLS) defects are among the most detrimental sources of loss and decoherence in superconducting quantum devices, and their microscopic nature still poorly understood. We develop a two-tone spectroscopy technique to characterize the spectral line width of TLS. This knowledge will help to distinguishes various types of TLS defects. In our experiments we use the fundamental TM010 pass band modes of 9-cell elliptical SRF cavities to probe spectral properties of TLS in native niobium oxide formed on the inside walls of the resonator. We pump one of the modes (4¿/9 through 8¿/9) with continuous high-power to saturate TLSs that couple to this frequency, and we probe the Q-factor of the ¿-mode. We observe increase of the quality factor of the probed ¿-mode when one of the neighboring modes is pumped. Extremely high quality factors of the pass band modes and their relative proximity in the frequency space allow us to estimate the width of the spectral hole burned in the TLS bath absorption spectrum which is related to the line spectral width of the TLS defects.
Measuring the internal quality factor of coplanar waveguide superconducting resonators is an established method of determining small losses in superconducting devices. Often, resonator losses are attributed to two-level system (TLS) defects using a power dependent model for the quality factor. However, excess non-equilibrium quasiparticles can also limit the quality factor of superconducting resonators. Here, a two-temperature, power and temperature dependent model is used to evaluate resonator losses for titanium nitride and aluminum coplanar waveguide resonators with loss tangents of 10−5–10−6. This model enables a set of parameters to describe both the internal quality factor and fractional frequency shift of the resonator across a broad range of average cavity photon numbers, from 1 to 106, and temperatures between those limited by the experimental apparatus near 50 mK and thermal quasiparticle dominated. The presented model also offers potential insight into observing the temperature and power dependence of TLS–TLS interactions in these resonators.
The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.
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