Coplanar Waveguide Resonators Research Articles

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.

Two-fluid physical modeling of superconducting resonators in the ARTEMIS framework

In this work, we implement a new London equation module for superconductivity in the GPU-enabled ARTEMIS framework, and couple it to a finite-difference time-domain solver for Maxwell's equations. We apply this two-fluid approach to model a superconducting coplanar waveguide (CPW) resonator. We validate our implementation by verifying that the theoretical skin depth and reflection coefficients can be obtained for several superconductive materials, with different London penetration depths, over a range of frequencies. Our convergence studies show that the algorithm is second-order accurate in both space and time, except at superconducting interfaces where the approach is spatially first-order. In our CPW simulations, we leverage the GPU scalability of our code to compare the two-fluid model to more traditional approaches that approximate superconducting behavior and demonstrate that superconducting physics can show comparable performance to the assumption of quasi-infinite conductivity as measured by the Q-factor.

Vortex dynamics in NbTi films at high frequency and high DC magnetic fields

We report on the characterization of NbTi films at sim 11 GHz and in DC magnetic fields up to 4 T, performed by means of the coplanar waveguide resonator technique, providing quantitative information about the penetration depth, the complex impedance, and the vortex-motion-induced complex resistivity. This kind of characterization is essential for the development of radiofrequency cavity technology. To access the vortex-pinning parameters, the complex impedance was analyzed within the formalism of the Campbell penetration depth. Measurements in this frequency range allowed us to determine the complete set of vortex-pinning parameters and the flux flow resistivity, both analyzed and discussed in the framework of high-frequency vortex dynamics models. The analysis also benefits from the comparison with results obtained by a dielectric-loaded resonator technique on similar samples and by other ancillary structural and electromagnetic characterization techniques that provide us with a comprehensive picture of the material. It turns out that the normalized flux flow resistivity follows remarkably well the trend predicted by the time dependent Ginzburg-Landau theory, while the pinning constant exhibits a decreasing trend with the field which points to a collective pinning regime.

Pure spin squeezing of h -BN spins coupled to superconducting resonator

The negatively charged boron vacancy (${\text{VB}}^{\ensuremath{-}}$) spin defect in two-dimensional (2D) hexagonal boron nitride ($h$-BN) has attracted much attention for potential applications in quantum photonics recently. Its inherent van der Waals force mechanism guarantees convenient heterostructures for quantum sensing. By virtue of such materials, researchers not only can fabricate enough thin spin film naturally close to the sensing target but also can prepare an almost perfect spin ensemble with a uniform orientation. We here propose a setup with an ensemble of ${\text{VB}}^{\ensuremath{-}}$ spins strongly coupled to the superconducting coplanar waveguide resonator through the magnetic-dipolar interaction. The collective coupling strength is predicted to be $G/2\ensuremath{\pi}\ensuremath{\sim}15$ MHz, which corresponds to the strong coupling region. This collective spin-photon interaction can mimic the one-axis twisting Lipkin-Meshkov-Glick model effectively and therefore guarantee the dynamic generation of the spin-squeezed state. In addition, we show the influence of inhomogeneous coupling caused by sample thickness on squeezing, which proves the validity of the homogeneity assumption in our scheme. This attempt not only explores the possibility and superiority of 2D ${\text{VB}}^{\ensuremath{-}}$ spins but also opens another avenue for quantum hybridization.

Realization of superconducting transmon qubits based on topological insulator nanowires

Topological-material-based Josephson junctions have the potential to be used to host Majorana zero modes and to construct topological qubits. For operating the topological qubits at an appropriate timescale to avoid decoherence and quasiparticle poisoning, one would eventually go to the time domain and embed the topological qubits into quantum electrodynamic circuits. Here, we constructed a topological-insulator-nanowire-based transmon qubit and demonstrated its strong coupling to a coplanar waveguide resonator. The flux-tunable spectrum and Rabi oscillations with a qubit lifetime T 1 of ∼ 0.5 μ s were observed. Such a hybrid platform, containing topological materials and quantum electrodynamic circuits, can further be used to study the physical properties such as Majorana zero modes in topological quantum circuits.

Chemical mechanical planarization for Ta-based superconducting quantum devices

We report on the development of a chemical mechanical planarization (CMP) process for thick damascene Ta structures with pattern feature sizes down to 100 nm. This CMP process is the core of the fabrication sequence for scalable superconducting integrated circuits at a 300 mm wafer scale. This work has established the elements of various CMP-related design rules that can be followed by a designer for the layout of circuits that include Ta-based coplanar waveguide resonators, capacitors, and interconnects for tantalum-based qubits and single flux quantum circuits. The fabrication of these structures utilizes a 193 nm optical lithography along with 300 mm process tools for dielectric deposition, reactive ion etch, wet-clean, CMP, and in-line metrology—all tools typical for a 300 mm wafer CMOS foundry. Theprocess development was guided by measurements of the physical and electrical characteristics of the planarized structures. Physical characterization such as atomic force microscopy across the 300 mm wafer surface showed that local topography was less than 5 nm. Electrical characterization confirmed low leakage at room temperature, and less than 12% within wafer sheet resistance variation for damascene Ta line widths ranging from 100 nm to 3 μm. Run-to-run reproducibility was also evaluated. Effects of process integration choices including the deposited thickness of Ta are discussed.

High-Resolution Dielectric Characterization of Single Cells and Microparticles Using Integrated Microfluidic Microwave Sensors

Microwave sensors can probe intrinsic material properties of analytes in a microfluidic channel at physiologically relevant ion concentrations. While microwave sensors have been used to detect single cells and microparticles in earlier studies, the synergistic use and comparative analysis of microwave sensors with optical microscopy for material classification and size tracking applications have been scarcely investigated so far. Here we combined microwave and optical sensing to differentiate microscale objects based on their dielectric properties. We designed and fabricated two types of planar sensor: a Coplanar Waveguide Resonator (CPW) and a Split-Ring Resonator (SRR). Both sensors possessed sensing electrodes with a narrow gap to detect single cells passing through a microfluidic channel integrated on the same chip. We also show that standalone microwave sensors can track the relative changes in cellular size in real-time. In sensing single 20-micron diameter polystyrene particles, Signal-to-Noise ratio values of approximately 100 for CPW and 70 for SRR sensors were obtained. These findings demonstrate that microwave sensing technology can serve as a complementary technique for single-cell biophysical experiments and microscale pollutant screening.

Vacuum Rabi Splitting and Kerr Effect of a Hybrid Spin–Magnon–Photon System

AbstractThe vacuum Rabi splitting and Kerr effect are investigated theoretically in a hybrid spin–magnon–photon system, where the nitrogen‐vacancy center in diamond driven by two light fields is coupled to a spherical micromagnet embedded in a superconducting coplanar waveguide resonator. The results indicate that the phenomenon of the Mollow triplet and vacuum Rabi splitting can appear by controlling the spin–magnon coupling and magnon–photon coupling. It is shown that the probe absorption spectrum can be adjusted effectively via the pump frequency detuning. Moreover, it is demonstrated that the optical Kerr effect can be tuned by changing the Rabi frequency. This work may provide a possibility for the applications in quantum information processing and quantum sensing of magnetic signal.

Superconducting Resonators with Voltage-Controlled Frequency and Nonlinearity

Voltage-tunable superconductor-semiconductor devices offer a unique platform to realize dynamic tunability in superconducting quantum circuits. By galvanically connecting a gated $\mathrm{In}\mathrm{As}$-$\mathrm{Al}$ Josephson junction to a coplanar waveguide resonator, we demonstrate the use of a superconducting element with wideband gate tunability. We show that the resonant frequency is controlled via a gate-tunable Josephson inductance and that the nonlinearity of the $\mathrm{In}\mathrm{As}$-$\mathrm{Al}$ junction is nondissipative as is the case with conventional ${\mathrm{Al}\mathrm{O}}_{\mathrm{x}}\text{-Al}$ junctions. As the gate voltage is decreased, the inductive participation of the junction increases up to $44\mathrm{%}$, resulting in the resonant frequency being tuned by over $2\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$. Utilizing the wide tunability of the device, we demonstrate that two resonant modes can be adjusted such that they strongly hybridize, exhibiting an avoided-level crossing with a coupling strength of $51\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. Implementing such voltage-tunable resonators is the first step toward realizing wafer-scale continuous voltage control in superconducting circuits for qubit-qubit coupling, quantum limited amplifiers, and quantum memory platforms.

Tunable Superconducting Flux Qubits with Long Coherence Times

In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\pm 3.5$ GHz around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain $T_{1}\sim 8 \mu s$. The echo dephasing times are limited by flux noise even at optimal points and reach $T_{2E}\sim 4 \mu s$, almost an order of magnitude longer than state of the art for tunable flux qubits.

Controllable Tunneling of Single Flux Quanta Mediated by Quantum Phase Slip in Disordered Superconducting Loops

Quantum phase-slip (QPS) is the exact dual to the well-known Josephson effect. Although there are numerous proposals for applications of QPS devices, experimental work to develop these remains in the relatively early stages. Significant barriers to exploiting QPS nanowires for useful technologies still exist, such as establishing robust nanowire fabrication methods that allow coupling to low-loss circuits, and demonstrating control over the QPS process with an experimenter-controlled external bias. Here we report experiments which show that both of these barriers have been overcome. We present measurements at 300 mK of NbN coplanar waveguide (CPW) resonators embedded with nanowires fabricated using a neon focused ion-beam. The internal quality factor exceeds $2\times10^{4}$ -- significantly higher than previously reported in comparable experiments. The resonator frequency tunes periodically with an applied magnetic field, revealing tunnelling of the order parameter that always occurs at half-integer values of the applied flux. In contrast to previous studies of single QPS, the order-parameter tunnelling is shown to be adiabatic, demonstrating improved control over energy dissipation in nanowire QPS circuits. Our results highlight a promising pathway towards realising low-loss nanowire-based QPS devices.

Fabrication and characterization of magnetic-field-resilient MoRe superconducting coplanar waveguide resonators

Magnetic-field-resilient superconducting coplanar waveguide (SCPW) resonators are essential for developing integrated quantum circuits. Molybdenum–Rhenium (MoRe), which is a disordered superconducting alloy forming a highly transparent contact to the graphene and carbon nanotubes, would be a promising platform for realizing the field-resilient SCPW resonators combined with nano-hybrid quantum devices. We fabricated MoRe SCPW resonators and investigated their microwave transmission characteristics with varying temperature and external magnetic field. The thickness of MoRe film is a critical parameter determining the lower critical field, kinetic inductance, and characteristic impedance of the SCPW resonator, resulting in drastic changes in the quality factor and the resonance frequency. We obtained a maximum value of Qi > 104 in parallel magnetic fields up to B|| = 0.15 T for the 27-nm-thick MoRe resonator. Our observations suggest that the MoRe SCPW resonator would be useful for integrating nano-hybrid spin or gatemon qubits and for developing spin-ensemble quantum memory devices.

Surface Passivation of Niobium Superconducting Quantum Circuits Using Self-Assembled Monolayers

Superconducting coplanar waveguide (CPW) microwave resonators in quantum circuits are the best components for reading and changing the state of artificial atoms because of their excellent coupling to quantum systems. This coupling forms the basis of the developing circuit quantum electrodynamic architecture. In quantum processors, oscillators are used to store and transmit quantum information using microwave-frequency wave packets. However, the presence of amorphous thin-film defects is deleterious and can result in an irrevocable loss of coherent information with uncontrolled degrees of freedom. Although there has been extensive research into techniques to reduce the coherent loss of such devices, the precise structure of amorphous dielectric layers on surfaces and interfaces and their associated loss mechanism are being actively studied. In particular, planar superconducting resonators are very sensitive to defects on their surfaces, such as two-level systems in oxidized metals and nonequilibrium quasiparticles, making these devices suitable probes for the different loss mechanisms. In this work, we present the design, fabrication, and characterization of Nb CPW resonators with different surface treatments with self-assembled monolayers (SAMs), which mitigate the growth of oxides in superconducting circuits. We demonstrate SAM-passivated resonators having internal quality factors of greater than 106 at a single-photon excitation power (measured at 100 mK), which were probed using scanning electron microscopy, X-ray photoelectron spectroscopy, and transmission electron microscopy to demonstrate the efficiency of our surface treatment. Finally, we compared the improvements in the experimental quality factors to those obtained by numerical simulation.

Tantalum microwave resonators with ultra-high intrinsic quality factors

We acquire tantalum thin film in its α phase (α-Ta) using direct-current magnetron sputtering. According to x-ray diffraction results, 110-Ta is dominant. Quarter-wavelength coplanar waveguide resonators are fabricated with the α-Ta film and characterized at millikelvin in a dilution refrigerator. In the single photon regime, an intrinsic quality factor (Qi) up to 3×106 is obtained in these resonators. At high power, Qi rises to 6×106. Moreover, we also fabricate an array with 7 × 7 lumped element resonators using the α-Ta film. The array shows excellent uniformity. At high power, Qis of all pixels exceed 1×106. In the single photon regime, Qis of over 90% pixels exceed 1×106. Superconducting quantum computing and ultrasensitive electromagnetic wave detectors will benefit a lot from devices based on the α-Ta film.

Size Reduction and Performance Enhancement of Coplanar-Waveguide Resonators for Surface Plasmonic Applications

Coplanar waveguide (CPW) is partially integrated with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -strip TLs at critical areas with locally strong electromagnetic field confinement. The new integration is shown to impact the propagation constant of the structure.The impacts of the added <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -strip TL are theoretically discussed on a loaded CPW using the incident-reflected wave concept. It is mathematically shown that a specific phase is added to the phase of conventional CPWs by the proposed modification. The added phase is then used for physical size reduction and performance enhancement of the structure. Considering the propagation manipulation of the CPWs, the modified structure is researched as a unit cell for spoof surface plasmon polariton (SSPP).

Co-Design quantum simulation of nanoscale NMR

Quantum computers have the potential to efficiently simulate the dynamics of nanoscale NMR systems. In this work, we demonstrate that a noisy intermediate-scale quantum computer can be used to simulate and predict nanoscale NMR resonances. In order to minimize the required gate fidelities, we propose a superconducting application-specific Co-Design quantum processor that reduces the number of SWAP gates by over 90% for chips with more than 20 qubits. The processor consists of transmon qubits capacitively coupled via tunable couplers to a central co-planar waveguide resonator with a quantum circuit refrigerator (QCR) for fast resonator reset. The QCR implements the nonunitary quantum operations required to simulate nuclear hyperpolarization scenarios.

Terahertz monolithic integrated coplanar band‐pass filter based on slotline mode

AbstractIn this letter, a terahertz monolithic integrated planar band‐pass filter based on coplanar waveguide (CPW) resonators has been proposed. By adopting the feeding line in form of a slotline, the need for air‐bridges in traditional CPW filters is eliminated, achieving good integrability and reducing fabrication difficulty. To further improve the filtering performance, the defected ground structure is used in the design, introducing a finite transmission zero at the lower sideband. The filter is manufactured on the semi‐insulation silicon carbide (SiC) substrate, to fit the existing advanced GaN‐on‐SiC monolithic integration system. Measurement reveals the fractional band‐width of 5.7% at the center frequency of 279 GHz, with an insertion loss of 5.1 dB. With a volume of 500 × 400 × 50 μm (0.45 × 0.36 × 0.045 λ0), the proposed filter improves the performance of the planar filter operating at the terahertz band effectively.

Superconducting boron doped nanocrystalline diamond microwave coplanar resonator

A coplanar waveguide resonator (CPR) is presented for kinetic inductance (Lk) and penetration depth (λL) measurements of superconducting boron doped nanocrystalline diamond (B-NCD) at microwave frequencies of 0.4 to 1.2 GHz and at temperatures below 3 K. Using finite element modelling and experimental measurements, this work demonstrates that thin granular B-NCD films (thickness d≈ 500nm) on Si have a large penetration depth (λL≈3.8μm), and therefore an associated high kinetic inductance per square (Lk,□≈ 670 to 690 pH/□). These values are much larger than those typically obtained for films on single crystal diamond, which is likely due to the high granularity of the nanocrystalline films. Based on the measured Q factors of the structure, the calculated surface resistance is found to be around ≈ 1 to 6μΩ at T<2 K in the 0.4 to 1.2 GHz range, demonstrating the potential for granular B-NCD for high quality factor superconducting microwave resonators and highly sensitive kinetic inductance detectors.

Aluminum air bridges for superconducting quantum devices realized using a single-step electron-beam lithography process

In superconducting quantum devices, air bridges enable increased circuit complexity and density, and mitigate the risk of microwave loss arising from mode mixing. We implement aluminum air bridges using a simple process based on single-step electron-beam gradient exposure. The resulting bridges have sizes ranging from 20 µm to 100 µm, with a yield exceeding 99% for lengths up to 36 µm. When used to connect ground planes in coplanar waveguide resonators, the induced loss contributed to the system is negligible, corresponding to a loss per bridge less than 1.0×10−8. The bridge process is compatible with Josephson junctions and allows for the simultaneous creation of low loss bandages between superconducting layers.

Gate-Tunable Kinetic Inductance in Proximitized Nanowires

We report the detection of a gate-tunable kinetic inductance in a hybrid InAs/Al nanowire. For this purpose, we have embedded the nanowire into a quarter-wave coplanar waveguide resonator and measured the resonance frequency of the circuit. We find that the resonance frequency can be changed via the gate voltage that controls the electron density of the proximitized semiconductor and thus the nanowire inductance. Applying Mattis-Bardeen theory, we extract the gate dependence of the normal state conductivity of the nanowire, as well as its superconducting gap. Our measurements complement existing characterization methods for hybrid nanowires and provide a new and useful tool for gate-controlled superconducting electronics.