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arXiv:2506.08130 · Physical Review Applied

Broadband high-precision measurement of two-level-system loss using multiwavelength superconducting resonators

Cliff Chen, Shahriar Aghaeimeibodi, Yuki Sato, Matthew H. Matheny, Oskar J. Painter, Jiansong Gao

Published Dec 16, 2025• 0 citations
arXivHTMLPDF

Abstract

Two-level systems (TLSs) are known to be a dominant source of dissipation and decoherence in superconducting qubits. Superconducting resonators provide a convenient way to study TLS-induced loss due to easier design and fabrication in comparison with devices that include nonlinear elements such as Josephson junctions. However, precisely measuring TLS-induced loss in a resonator in the quantum regime is challenging due to low signal-to-noise ratio (SNR) and the temporal fluctuations of the TLS, leading to uncertainties of 20% or more in the loss measurement. To address these limitations, we develop a multiwavelength resonator device that extends the resonator length from a standard quarter wavelength λ / 4 to N λ / 4 , where N = 37 , at 6 GHz. This design provides two key advantages: the TLS-induced fluctuations are reduced by a factor of N due to spatial averaging over an increased number of independent TLSs, and the measurement SNR for a given intraresonator energy density increases by a factor of N . The multiwavelength resonator also has fundamental and harmonic resonances spanning a wide frequency range, allowing one to study the frequency dependence of TLS-induced loss. In this work we fabricate both multiwavelength and quarter-wave coplanar waveguide resonators formed from thin-film aluminum on a silicon substrate, and characterize their TLS properties at 10 and 200 mK. Our results show that the power-dependent TLS-induced loss measured from the N λ / 4 resonator agrees well with that measured from the λ / 4 resonator, while achieving a fivefold reduction in measurement uncertainty due to TLS fluctuations, down to 5 % . The N λ / 4 resonator also provides a measure of the fully unsaturated TLS-induced loss due to the increased measurement SNR at low intraresonator energy densities. Finally, measurements across seven harmonic resonances of the N λ / 4 resonator between 4 and 6.5 GHz reveal no frequency dependence in the TLS-induced loss over this range. These results highlight the benefits of the multiwavelength resonator approach for material development in superconducting quantum circuits.

DOI
10.1103/2l7h-zn9s

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Two-level systems (TLSs) are known to be a dominant source of dissipation and decoherence in superconducting qubits. Superconducting resonators provide a convenient way to study TLS-induced loss due to easier design and fabrication in comparison with devices that include nonlinear elements such as Josephson junctions. However, precisely measuring TLS-induced loss in a resonator in the quantum regime is challenging due to low signal-to-noise ratio (SNR) and the temporal fluctuations of the TLS, leading to uncertainties of 20% or more in the loss measurement. To address these limitations, we develop a multiwavelength resonator device that extends the resonator length from a standard quarter wavelength λ / 4 to N λ / 4 , where N = 37 , at 6 GHz. This design provides two key advantages: the TLS-induced fluctuations are reduced by a factor of N due to spatial averaging over an increased number of independent TLSs, and the measurement SNR for a given intraresonator energy density increases by a factor of N . The multiwavelength resonator also has fundamental and harmonic resonances spanning a wide frequency range, allowing one to study the frequency dependence of TLS-induced loss. In this work we fabricate both multiwavelength and quarter-wave coplanar waveguide resonators formed from thin-film aluminum on a silicon substrate, and characterize their TLS properties at 10 and 200 mK. Our results show that the power-dependent TLS-induced loss measured from the N λ / 4 resonator agrees well with that measured from the λ / 4 resonator, while achieving a fivefold reduction in measurement uncertainty due to TLS fluctuations, down to 5 % . The N λ / 4 resonator also provides a measure of the fully unsaturated TLS-induced loss due to the increased measurement SNR at low intraresonator energy densities. Finally, measurements across seven harmonic resonances of the N λ / 4 resonator between 4 and 6.5 GHz reveal no frequency dependence in the TLS-induced loss over this range. These results highlight the benefits of the multiwavelength resonator approach for material development in superconducting quantum circuits.
In current superconducting qubit circuit development, coherence time is limited by low-frequency flux noise introduced from localized two-level systems (TLSs) in the fabricated superconducting circuit, including superconducting materials, the interface between thin films, and the substrate. As a part of the effect to tackle this issue from a substrate standpoint, we succeed in fabricating NbN (200) oriented coplanar waveguide resonator (CPWR) on a thin titanium nitride (TiN) (200) buffered Si (100) substrate. The internal loss is close to 3 × 10-5nearphoton> ~1, improved from ~2 × 10-4in NbN (200) CPWR fabricated on MgO (100). For NbN (200) resonators grown on Si (100), the internal loss shows microwave energy independent. To further clarity if this energy independence is due to the change of substrate material, we also fabricated TiN (200) CPWR on Si (100). In contrast to NbN (200) CPWR, the loss of TiN (200) resonator shows a strong microwave dependent, an indication of TLSs originated from the interface and the surface. We suggest TLSs in NbN (200) CPWR are dominated from different mechanism other than arising from the interface and surface.
Material research is a key frontier in advancing superconducting qubit and circuit performance. In this work, we develop a simple and broadly applicable framework for accurately characterizing two-level system (TLS) loss using internal quality factor measurements of superconducting transmission line resonators over a range of temperatures and readout powers. We applied this method to a series of ααα-Ta resonators that span a wide frequency range, thus providing a methodology for probing the loss mechanisms in the fabrication process of this emerging material for superconducting quantum circuits. We introduce an analytical model that captures the loss behavior without relying on numerical simulations, enabling straightforward interpretation and calibration. Additionally, our measurements reveal empirical frequency-dependent trends in key parameters of the model, suggesting contributions from mechanisms beyond the standard tunneling model of TLSs.
The performance of superconducting circuits for quantum computing is limited by materials losses. In particular, coherence times are typically bounded by two-level system (TLS) losses at single photon powers and millikelvin temperatures. The identification of low loss fabrication techniques, materials, and thin film dielectrics is critical to achieving scalable architectures for superconducting quantum computing. Superconducting microwave resonators provide a convenient qubit proxy for assessing performance and studying TLS loss and other mechanisms relevant to superconducting circuits such as non-equilibrium quasiparticles and magnetic flux vortices. In this review article, we provide an overview of considerations for designing accurate resonator experiments to characterize loss, including applicable types of losses, cryogenic setup, device design, and methods for extracting material and interface losses, summarizing techniques that have been evolving for over two decades. Results from measurements of a wide variety of materials and processes are also summarized. Finally, we present recommendations for the reporting of loss data from superconducting microwave resonators to facilitate materials comparisons across the field.
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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
Superconducting resonators are widely used in many applications such as qubit readout for quantum computing applications, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms under microwave excitation, especially the dissipation due to non-equilibrium quasi-particles and two-level systems (TLS), which can result in a decrease of the superconducting intrinsic quality factor (QiQ_iQi​) in high quality superconducting resonators. Particularly in the few-photon and low temperature (T) regime, TLS losses can become a dominant loss mechanism. In this study, novel aluminum half-wavelength resonators are investigated, focusing on the loss properties at extra-low power and low temperature. An unusual increase of Qi(T)Q_i(T)Qi​(T) with deceasing temperature is observed. This behavior is attributed to the increase of TLS coherence time (T2T_2T2​) at ultra-low temperatures and powers. This T2T_2T2​ increase is consistent with other work on resonant frequency noise in resonators and measurements of individual TLS, and likely arises from interacting TLS in the aluminum half-wavelength resonators.