Coplanar Waveguide Resonators Research Articles

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.

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.

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

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.

High-Q trenched aluminum coplanar resonators with an ultrasonic edge microcutting for superconducting quantum devices

Dielectric losses are one of the key factors limiting the coherence of superconducting qubits. The impact of materials and fabrication steps on dielectric losses can be evaluated using coplanar waveguide (CPW) microwave resonators. Here, we report on superconducting CPW microwave resonators with internal quality factors systematically exceeding 5 × 106 at high powers and 2 × 106 (with the best value of 4.4 × 106) at low power. Such performance is demonstrated for 100-nm-thick aluminum resonators with 7–10.5 um center trace on high-resistivity silicon substrates commonly used in Josephson-junction based quantum circuit. We investigate internal quality factors of the resonators with both dry and wet aluminum etching, as well as deep and isotropic reactive ion etching of silicon substrate. Josephson junction compatible CPW resonators fabrication process with both airbridges and silicon substrate etching is proposed. Finally, we demonstrate the effect of airbridges’ positions and extra process steps on the overall dielectric losses. The best quality factors are obtained for the wet etched aluminum resonators and isotropically removed substrate with the proposed ultrasonic metal edge microcutting.

Investigation of the deposition of α-tantalum (110) films on a-plane sapphire substrate by molecular beam epitaxy for superconducting circuit

Polycrystalline α-tantalum (110) films deposited on the c-plane sapphire substrate by sputtering are used in superconducting qubits nowadays. However, these films always occasionally form other structures, such as α-tantalum (111) grains and β-tantalum grains. To improve the film quality, we investigate the growth of α-tantalum (110) films on the a-plane sapphire substrate under varying conditions by molecular beam epitaxy technology. The optimized α-tantalum (110) film is a single crystal, with a smooth surface and atomically flat metal–substrate interface. The film with thickness of 30 nm shows a Tc of 4.12 K and a high residual resistance ratio of 9.53. The quarter wavelength coplanar waveguide resonators fabricated with the 150 nm optimized α-tantalum (110) film exhibit intrinsic quality factor of over one million under single photon excitation at millikelvin temperature.

Hybrid quantum systems with high-T_c superconducting resonators

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T_c superconductors are mainly employed, high-T_c cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of textrm{YBa}_2textrm{Cu}_3textrm{O}_{7-delta } superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T_c superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.

Post-fabrication frequency trimming of coplanar-waveguide resonators in circuit QED quantum processors

We present the use of a set of airbridges to trim the frequency of microwave coplanar-waveguide (CPW) resonators post-fabrication. This method is compatible with the fabrication steps of conventional CPW airbridges and crossovers and increases device yield by allowing compensation of design and fabrication uncertainty with 100 MHz range and 10 MHz resolution. We showcase two applications in circuit QED. The first is the elimination of frequency collisions between resonators intended to readout different transmons by frequency-division multiplexing. The second is frequency matching of readout and Purcell-filter resonator pairs. Combining this matching with transmon frequency trimming by laser annealing reliably achieves fast and high-fidelity readout across 17-transmon quantum processors.

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator (lambda /4 CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency omega _{textrm{cutoff}} for the coupling between the FQ and the modes in the CPWR, where the coupling grows as sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}ll 1 and decreases as 1/sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}gg 1. Here omega _n is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above omega _{textrm{cutoff}} at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.

Spectroscopic studies of the superconducting gap in the 12442 family of iron-based compounds (Review article)

The iron-based compounds of the so-called 12442 family are very peculiar in various respects. They originate from the intergrowth of 122 and 1111 building blocks, display a large in-plane vs out-of-plane anisotropy, possess double layers of FeAs separated by insulating layers, and are generally very similar to double-layer cuprates. Moreover, they are stoichiometric superconductors because of an intrinsic hole doping. Establishing their superconducting properties, and in particular the symmetry of the order parameter, is thus particularly relevant in order to understand to what extent these compounds can be considered as the iron-based counterpart of cuprates. In this work, we review the results of various techniques from the current literature and compare them with ours, obtained in Rb–12442 by combining point-contact Andreev reflection spectroscopy and coplanar waveguide resonator measurements of the superfluid density. It turns out that the compound possesses at least two gaps, one of which is certainly nodal. The compatibility of this result with the theoretically allowed gap structures, as well as with the other results in literature, is discussed in detail.

Stepwise Fabrication and Optimization of Coplanar Waveguide Resonator Hybrid Devices

From the background of microwave‐optomechanical experiments involving carbon nanotubes, the optimization of superconducting coplanar waveguide resonator devices is discussed. Two devices, one with unmodified geometry compared to previous work and one integrating several improvements, are lithographically built up step‐by‐step. After each step, the low‐temperature GHz transmission properties are retested. This allows to identify the impact of the fabrication and the geometry modification on the device properties. In addition, simplified circuit geometries are modeled numerically, confirming the experimental results and providing further insights for optimization.