Coplanar Waveguide Resonators Research Articles

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

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

Controllable coupling between fundamental modes in an asymmetric superconducting coplanar waveguide resonator

Controllable coupling between the odd and even fundamental modes of an asymmetric half-wavelength superconducting coplanar waveguide resonator is demonstrated. The resonant frequency of the even mode Ωe could be tuned by an external magnetic field, while the resonant frequency of the odd mode Ωo is field independent. To realize the tunability of Ωe, the central conductor of the NbN-based resonator was galvanically coupled to an array of Al-based rf-SQUIDs (radio frequency superconducting quantum interferometer device). These rf-SQUIDs are placed in only one resonator gap, ensuring its strong asymmetry. By adjusting the appropriate external magnetic flux Φ, equal frequencies of both modes were obtained. At this resonant point Ωo(Φ)=Ωe(Φ) an avoided level crossing of the eigenfrequencies was observed, demonstrating the coupling between the odd and even fundamental modes.

Dynamics and resonance fluorescence from a superconducting artificial atom doubly driven by quantized and classical fields

We report an experimental demonstration of resonance fluorescence in a two-level superconducting artificial atom under two driving fields coupled to a detuned cavity. One of the fields is classical and the other is varied from quantum (vacuum fluctuations) to classical by controlling the photon number inside the cavity. The device consists of a transmon qubit strongly coupled to a one-dimensional transmission line and a coplanar waveguide resonator. We observe a sideband anticrossing and asymmetry in the emission spectra of the system through a one-dimensional transmission line, which is fundamentally different from the weak-coupling case. By changing the photon number inside the cavity, the emission spectrum of our doubly driven system approaches the case when the atom is driven by two classical bichromatic fields. We also measure the dynamical evolution of the system through the transmission line and study the properties of the first-order correlation function, Rabi oscillations, and energy relaxation in the system. The study of resonance fluorescence from an atom driven by two fields promotes understanding decoherence in superconducting quantum circuits and may find applications in superconducting quantum computing and quantum networks. Published by the American Physical Society 2024

Exploring the relationship between deposition method, microstructure, and performance of Nb/Si-based superconducting coplanar waveguide resonators

Superconducting quantum circuits (SQC) are one of the most promising hardware platforms for quantum computing, yet their performance is currently limited by the presence of various structural defects inside the circuit's structure. Despite impressive progress in the past decade, a precise understanding of the origin of these defects from various fabrication processes and their impact on coherence is still lacking. In this study, we performed a comprehensive investigation on the microstructure, superconductivity, and resonator quality factor of Nb films deposited by high-power impulse magnetron sputtering (HiPIMS) and direct current (DC) magnetron sputtering. A suite of characterization techniques, including electron microscopy with spectroscopy, secondary ion mass spectrometry, magneto-optical microscopy, and pump-probe reflectivity spectroscopy is used. We reveal that niobium (Nb) resonators fabricated using HiPIMS exhibit a smaller average grain size, thicker surface oxide with larger thickness variations (rougher surface), and a thicker amorphous Nb/Si interface layer compared to samples deposited by DC sputtering. We identified that the amorphous Nb oxides (mainly located at the Nb surface and along the grain boundaries) and Nb-Si amorphous layers (at the Nb/Si interface) are major and potential sources of two-level system (TLS), while off-stochiometric oxides and suboxides of Nb close to the surface, crystalline defects (i.e., dislocations at grain boundary, point defects introduced during deposition) are main contributors of non-TLS sources. Our findings clarify the relationship between different defects and coherence loss mechanisms, highlighting the importance of material microstructure control on performance optimization in SQC.

A Novel Microwave Sensor System Based on Feedback-Type Oscillator and Modified Coplanar Waveguide Resonator for Retrieving Complex Permittivity of Liquid Samples

A Novel Microwave Sensor System Based on Feedback-Type Oscillator and Modified Coplanar Waveguide Resonator for Retrieving Complex Permittivity of Liquid Samples

Demonstration of Microwave Resonators and Double Quantum Dots on Optimized Reverse-Graded Ge/SiGe Heterostructures.

One of the most promising platforms for the realization of spin-based quantum computing are planar germanium quantum wells embedded between silicon-germanium barriers. To achieve comparably thin stacks with little surface roughness, this type of heterostructure can be grown using the so-called reverse linear grading approach, where the growth starts with a virtual germanium substrate followed by a graded silicon-germanium alloy with an increasing silicon content. However, the compatibility of such reverse-graded heterostructures with superconducting microwave resonators has not yet been demonstrated. Here, we report on the successful realization of well-controlled double quantum dots and high-quality coplanar waveguide resonators on the same reverse-graded Ge/SiGe heterostructure.

Low-loss liquid metal interconnects for superconducting quantum circuits

Building a modular architecture with superconducting quantum computing chips is one of the means to achieve qubit scalability, allowing the screening, selection, replacement, and integration of individual qubit modules into large quantum systems. However, the nondestructive replacement of modules within a compact architecture remains a challenge. Liquid metals, specifically gallium alloys, can be alternatives to solid-state galvanic interconnects. This is motivated by their self-healing, self-aligning, and other desirable fluidic properties, potentially enabling the nondestructive replacement of modules at room temperatures, even after operating the entire system at millikelvin regimes. In this study, we present coplanar waveguide resonators (CPWRs) interconnected by gallium alloy droplets, achieving high internal quality factors up to nearly one million and demonstrating performance on par with the continuous solid-state CPWRs. Leveraging the desirable fluidic properties of gallium alloys at room temperature and their compact design, we envision a modular quantum system enabled by liquid metals.

Phase-Slip Based SQUID Used as a Photon Switch in Superconducting Quantum Computation Architectures

The photon storage time in a superconducting coplanar waveguide (CPW) resonator is contingent on the loaded quality factor, primarily dictated by the input and output capacitance of the resonator. The phase-slip based superconducting quantum interference device (PS-SQUID) comprises two phase-slip (PS) junctions connected in series with a superconducting island in between. The PS-SQUID can manifest nonlinear capacitance behavior, with the capacitance finetuned by the gate voltage to minimize the impact of magnetic field noise as much as possible. By substituting the coupling capacitance of the CPW resonator with the PS-SQUID, the loaded quality factor of the resonator can be changed by three orders, thus, we get a microwave photon switch in superconducting quantum computation architectures. Furthermore, by regulating the loaded quality factors, the coupling strength between the CPW and superconducting quantum circuits can be controlled, enabling the ability to manipulate stationary qubits and flying qubits.

Characterization of process-related interfacial dielectric loss in aluminum-on-silicon by resonator microwave measurements, materials analysis, and imaging

We systematically investigate the influence of the fabrication process on dielectric loss in aluminum-on-silicon superconducting coplanar waveguide resonators with internal quality factors (Qi) of about one million at the single-photon level. These devices are essential components in superconducting quantum processors; they also serve as proxies for understanding the energy loss of superconducting qubits. By systematically varying several fabrication steps, we identify the relative importance of reducing loss at the substrate–metal and substrate–air interfaces. We find that it is essential to clean the silicon substrate in hydrogen fluoride (HF) prior to aluminum deposition. A post-fabrication removal of the oxides on the surface of the silicon substrate and the aluminum film by immersion in HF further improves the Qi. We observe a small, but noticeable, adverse effect on the loss by omitting either standard cleaning (SC1), pre-deposition heating of the substrate to 300 °C, or in situ post-deposition oxidation of the film’s top surface. We find no improvement due to excessive pumping meant to reach a background pressure below 6 × 10−8 mbar. We correlate the measured loss with microscopic properties of the substrate–metal interface through characterization with x-ray photoelectron spectroscopy, time-of-flight secondary ion mass spectrometry, transmission electron microscopy, energy-dispersive x-ray spectroscopy, and atomic force microscopy.

Low-loss α-tantalum coplanar waveguide resonators on silicon wafers: fabrication, characterization and surface modification

The performance of state-of-the-art superconducting quantum devices is currently limited by microwave dielectric loss at different interfaces. α-tantalum is a superconductor that has proven effective in reducing dielectric loss and improving device performance due to its thin low-loss oxide. Here, we demonstrate the fabrication of high-quality factor α-tantalum coplanar-waveguide resonators directly on pristine 300 mm silicon wafers over a variety of metal deposition conditions and perform a comprehensive material and electrical characterization study. Additionally, we apply a surface treatment based on hydrofluoric acid that allows us to modify different resonators surfaces, leading to a reduction in two-level system loss in the devices by a factor of three. This loss reduction can be entirely attributed to the removal of surface oxides. Our study indicates that large scale manufacturing of low-loss superconducting circuits should indeed be feasible and suggests a viable avenue to materials-driven advancements in superconducting circuit performance.

Formation and Microwave Losses of Hydrides in Superconducting Niobium Thin Films Resulting from Fluoride Chemical Processing

AbstractSuperconducting niobium (Nb) thin films have recently attracted significant attention due to their utility for quantum information technologies. In the processing of Nb thin films, fluoride‐based chemical etchants are commonly used to remove surface oxides that are known to affect superconducting quantum devices adversely. However, these same etchants can also introduce hydrogen to form Nb hydrides, potentially negatively impacting microwave loss performance. Here, comprehensive materials characterization of Nb hydrides formed in Nb thin films as a function of fluoride chemical treatments is presented. In particular, secondary‐ion mass spectrometry, X‐ray scattering, and transmission electron microscopy reveal the spatial distribution and phase transformation of Nb hydrides. The rate of hydride formation is determined by the fluoride solution acidity and the etch rate of Nb2O5, which acts as a diffusion barrier for hydrogen into Nb. The resulting Nb hydrides are detrimental to Nb superconducting properties and lead to increased power‐independent microwave loss in coplanar waveguide resonators. However, Nb hydrides do not correlate with two‐level system loss or device aging mechanisms. Overall, this work provides insight into the formation of Nb hydrides and their role in microwave loss, thus guiding ongoing efforts to maximize coherence time in superconducting quantum devices.

Coherent interface between optical and microwave photons on an integrated superconducting atom chip

Sub-wavelength arrays of atoms exhibit remarkable optical properties, analogous to those of phased array antennas, such as collimated directional emission or nearly perfect reflection of light near the collective resonance frequency. We propose to use a single-sheet sub-wavelength array of atoms as a switchable mirror to achieve a coherent interface between propagating optical photons and microwave photons in a superconducting coplanar waveguide resonator. In the proposed setup, the atomic array is located near the surface of the integrated superconducting chip containing the microwave cavity and optical waveguide. A driving laser couples the excited atomic state to Rydberg states with strong microwave transition. Then the presence or absence of a microwave photon in the superconducting cavity makes the atomic array transparent or reflective to the incoming optical pulses of proper frequency and finite bandwidth.

Control and readout of a transmon using a compact superconducting resonator

We demonstrate control and readout of a superconducting artificial atom based on a transmon qubit using a compact lumped-element resonator. The resonator consists of a parallel-plate capacitor with a wire geometric inductor. The footprint of the resonators is about 200 × 200 μm2, which is similar to the standard transmon size and one or two orders of magnitude more compact in the occupied area compared to coplanar waveguide resonators. We observe coherent Rabi oscillations and obtain time-domain properties of the transmon. The work opens a door to miniaturize essential components of superconducting circuits and to further scale up quantum systems with superconducting transmons.

Tunable superconducting resonators via on-chip control of local magnetic field

Abstract Superconducting microwave resonators play a pivotal role in superconducting quantum circuits. The ability to fine-tune their resonant frequencies provides enhanced control and flexibility. Here, we introduce a frequency-tunable superconducting coplanar waveguide resonator. By applying electrical currents through specifically designed ground wires, we achieve the generation and control of a localized magnetic field on the central line of the resonator, enabling continuous tuning of its resonant frequency. We demonstrate a frequency tuning range of 54.85 MHz in a 6.21 GHz resonator. This integrated and tunable resonator holds great potential as a dynamically tunable filter and as a key component of communication buses and memory elements in superconducting quantum computing.

Stable and low loss oxide layer on α-Ta (110) film for superconducting qubits

The presence of amorphous oxide layers can significantly affect the coherent time of superconducting qubits due to their high dielectric loss. Typically, the surface oxides of superconductor films exhibit lossy and unstable behavior when exposed to air. To increase the coherence time, it is essential for qubits to have stable and low dielectric loss oxides, either as barrier or passivation layers. In this study, we highlight the robust and stable nature of an amorphous tantalum oxide layer formed on α-Ta (110) film by employing chemical and structural analyses. Such kind of oxide layer forms in a self-limiting process on the surface of α-Ta (110) film in piranha solution, yielding stable thickness and steady chemical composition. Quarter-wavelength coplanar waveguide resonators are made to study the loss of this oxide. One resonator has a Qi of 3.0 × 106 in the single photon region. The Qi of most devices are higher than 2.0 × 106. Moreover, most of them are still over 1 × 106 even after exposed to air for months. Based on these findings, we propose an all-tantalum superconducting qubit utilizing such oxide as passivation layers, which possess low dielectric loss and improved stability.

Permittivity and Concentration Measurements Based on Coplanar Waveguide and Split Ring Resonator Sensor

Permittivity and Concentration Measurements Based on Coplanar Waveguide and Split Ring Resonator Sensor

Microwave characterization of tantalum superconducting resonators on silicon substrate with niobium buffer layer

Tantalum thin films sputtered on unheated silicon substrates are characterized with microwaves at around 10 GHz in a 10 mK environment. We show that the phase of tantalum with a body-centered cubic lattice (α-Ta) can be grown selectively by depositing a niobium buffer layer prior to a tantalum film. The physical properties of the films, such as superconducting transition temperature and crystallinity, change markedly with the addition of the buffer layer. Coplanar waveguide resonators based on the composite film exhibit significantly enhanced internal quality factors compared with a film without the buffer layer. The internal quality factor approaches 2 × 107 at a large-photon-number limit. While the quality factor decreases at the single-photon level owing to two-level system (TLS) loss, we have deduced that one of the causes of TLS loss is the amorphous silicon layer at the film–substrate interface, which originates from the substrate cleaning before the film deposition rather than the film itself. The temperature dependence of the internal quality factors shows a marked rise below 200 mK, suggesting the presence of TLS–TLS interactions. The present low-loss tantalum films can be deposited without substrate heating and thus have various potential applications in superconducting quantum electronics.

Improved parameter targeting in 3D-integrated superconducting circuits through a polymer spacer process

Three-dimensional device integration facilitates the construction of superconducting quantum information processors with more than several tens of qubits by distributing elements such as control wires, qubits, and resonators between multiple layers. The frequencies of resonators and qubits in flip-chip-bonded multi-chip modules depend on the details of their electromagnetic environment defined by the conductors and dielectrics in their vicinity. Accurate frequency targeting therefore requires precise control of the separation between chips and minimization of their relative tilt. Here, we describe a method to control the inter-chip separation by using polymer spacers. With the spacers, we measure a mean tilt of (76 ± 36) μrad, and a mean deviation of (0.4 ± 0.8) μm from the target inter-chip separation of 10 μm. We apply this process to coplanar waveguide resonator samples and observe chip-to-chip resonator frequency variations below 50 MHz (≈1%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\approx 1\\%$\\end{document}). We measure internal quality factors of 5×105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$5\ imes10^{5}$\\end{document} at the single-photon level, suggesting that the added spacers are compatible with low-loss device fabrication.

Compact dual‐band bandpass filter based on EMSICC and CPW resonator with excellent design flexibility

AbstractIn this letter, a novel dual‐band bandpass filter (BPF) with independently controllable center frequencies, bandwidths, and transmission zeros (TZs) is presented. The proposed BPF is realized by using eighth‐mode substrate‐integrated circular cavities (EMSICCs) and coplanar waveguide (CPW) resonators. The CPW resonators are embedded in the upper surface of the EMSICCs, allowing for a compact size without additional circuit dimensions. Finally, a dual‐band BPF for WLAN is designed and fabricated with center frequencies of 2.45 and 5.2 GHz. The measured results closely align with the simulated ones, validating the performance of the filter. Multiple TZs are generated by cross‐coupling and source‐load coupling, which results in good out‐of‐band rejection performance.

Anomalous Loss Reduction Below Two‐Level System Saturation in Aluminum Superconducting Resonators

AbstractSuperconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two‐level systems (TLS) which become the dominant source of loss in the few‐photon and low temperature regime. In this study, capacitively‐coupled aluminum half‐wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.