Superconducting Resonator Research Articles

One-step entanglements generation on distant superconducting resonators in the dispersive regime

We present a scalable quantum-bus-based device for generating the entanglement on photons in distant superconducting resonators (SRs). The device is composed of some one-dimensional (1D) SRs $$r_j$$ coupled to the quantum bus (another common resonator R) in its different positions assisted by superconducting quantum interferometer devices which are used to tune the coupling strengths between $$r_j$$ and R. By using the technique for catching and releasing a photon state in a 1D SR, it can work as an entanglement generator or a node in quantum communication. To demonstrate the performance of this device, we propose a one-step scheme to generate high-fidelity Bell state on photons in two distant SRs. It works in the dispersive regime of $$r_j$$ and R, which enables us to extend it to generate high-fidelity multi-Bell states on different resonator pairs simultaneously.

Period-tripling subharmonic oscillations in a driven superconducting resonator

We have observed period-tripling subharmonic oscillations in a driven superconducting coplanar waveguide resonator operated in the quantum regime, ${k}_{B}T\ensuremath{\ll}\ensuremath{\hbar}\ensuremath{\omega}$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\ensuremath{\omega}/2\ensuremath{\pi}\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$, when driving the resonator with a current at $3\ensuremath{\omega}$, with amplitude exceeding an instability threshold. We observed three stable radiative states with equal amplitudes, phase shifted by $2\ensuremath{\pi}/3$ rad, red detuned from the fundamental mode. The down-conversion from $3\ensuremath{\omega}$ to $\ensuremath{\omega}$ is strongly enhanced by near-resonant excitation of the second mode of the resonator and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.

Strong coupling of magnons in a YIG sphere to photons in a planar superconducting resonator in the quantum limit

We report measurements made at millikelvin temperatures of a superconducting coplanar waveguide resonator (CPWR) coupled to a sphere of yttrium-iron garnet. Systems hybridising collective spin excitations with microwave photons have recently attracted interest for their potential quantum information applications. In this experiment the non-uniform microwave field of the CPWR allows coupling to be achieved to many different magnon modes in the sphere. Calculations of the relative coupling strength of different mode families in the sphere to the CPWR are used to successfully identify the magnon modes and their frequencies. The measurements are extended to the quantum limit by reducing the drive power until, on average, less than one photon is present in the CPWR. Investigating the time-dependent response of the system to square pulses, oscillations in the output signal at the mode splitting frequency are observed. These results demonstrate the feasibility of future experiments combining magnonic elements with planar superconducting quantum devices.

Transmission-line resonators for the study of individual two-level tunneling systems

Parasitic two-level tunneling systems (TLS) emerge in amorphous dielectrics and constitute a serious nuisance for various microfabricated devices, where they act as a source of noise and decoherence. Here, we demonstrate a new test bed for the study of TLS in various materials which provides access to properties of individual TLS as well as their ensemble response. We terminate a superconducting transmission-line resonator with a capacitor that hosts TLS in its dielectric. By tuning TLS via applied mechanical strain, we observe the signatures of individual TLS strongly coupled to the resonator in its transmission characteristics and extract the coupling components of their dipole moments and energy relaxation rates. The strong and well-defined coupling to the TLS bath results in pronounced resonator frequency fluctuations and excess phase noise, through which we can study TLS ensemble effects such as spectral diffusion, and probe theoretical models of TLS interactions.

Implementing a universal gate set on a logical qubit encoded in an oscillator

A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and precise control over the entire system. Whether based on multiple physical qubits or larger dimensional modes such as oscillators, the individual elements in realistic devices will always have residual interactions, which must be accounted for when designing logical operations. Here we demonstrate a holistic control strategy which exploits accurate knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system. We use this approach to realize high-fidelity (98.5%, inferred), decoherence-limited operations on a logical qubit encoded in a superconducting cavity resonator using four-component cat states. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing.

Superconductive Ultracompact Magnetically Coupled Resonator With Twin-Spiral Structure

We describe a practical design of an ultracompact on-chip superconductive microresonator as a potential magnetic element of metamaterial. The achieved resonator size with respect to the wavelength in our experiment is about λ /14 400. The resonator consists of two superconducting Nb spirals, sandwiched face to face, with a small gap filled with dielectric. The spirals are turning in opposite directions: one clockwise, another counterclockwise. We study the resonator spectral response and its inner modes using numerical simulation in HFSS. In experiment with a laser scanning microscope, we confirm the predictions for the resonance frequencies of Nb superconductive resonator and its inner modes structures. Small size and the ease of manufacturing make the two-spiral resonator an attractive solution for superconductive filters, coupling circuits, and as a magnetic component of a metamaterial.

Relaxation of Microwave Nonlinearity in a Cuprate Superconducting Resonator

The 2nd and 3rd order nonlinear microwave response of a superconducting YBa2Cu3O7 thin film resonator was synchronously measured using three input tones. This technique permits the local measurement, and hence mapping, of intermodulation distortion (IMD) inside the resonator. 2nd and 3rd order IMD measured with a fixed probe relaxed in remarkably different ways after the removal of a static magnetic field. The 2nd order IMD relaxed by two different magnetic processes, a fast process that appears related to bulk remanent magnetization, and a slow process that fits the description of Bean and Livingston. The 3rd order IMD relaxes by only one process which is distinct from the two processes controlling 2nd order relaxation.

Suppression of multipacting in high power RF couplers operating with superconducting cavities

Capacitive input couplers based on a 50Ω coaxial transmission line are frequently used to transmit RF power to superconducting (SC) resonators operating in CW mode. It is well known that coaxial transmission lines are prone to multipacting phenomenon in a wide range of RF power level and operating frequency. The Facility for Rare Isotope Beams (FRIB) being constructed at Michigan State University includes two types of quarter wave SC resonators (QWR) operating at 80.5MHz and two types of half wave SC resonators (HWR) operating at 322MHz. As was reported in ref. [1] a capacitive input coupler used with HWRs was experiencing strong multipacting that resulted in a long conditioning time prior the cavity testing at design levels of accelerating fields. We have developed an insert into 50Ω coaxial transmission line that provides opportunity to bias the RF coupler antenna and protect the amplifier from the bias potential in the case of breakdown in DC isolation. Two of such devices have been built and are currently used for the off-line testing of 8 HWRs installed in the cryomodule.

Inductively-coupled Frequency Tuning and Impedance Matching in HTS-based NMR Probes.

Nuclear Magnetic Resonance (NMR) probes based on High Temperature Superconducting (HTS) resonators have demonstrated significant gains in detection sensitivity. However, the widespread acceptance of this technology has been limited by some unresolved issues including the mechanical unreliability of the moveable inductive loops used to adjust tuning and matching. In order to improve reliability, we propose to implement frequency tuning and impedance matching of HTS resonators using fixed inductively coupled loops and variable capacitors. By analyzing the loss mechanisms associated with inductive loops, we predict that using a superconducting inductive loop for tuning and matching will not only improve the reliability of HTS probes, but also provide improvements in sensitivity.

Observation of Collective Coupling between an Engineered Ensemble of Macroscopic Artificial Atoms and a Superconducting Resonator.

The hybridization of distinct quantum systems is now seen as an effective way to engineer the properties of an entire system leading to applications in quantum metamaterials, quantum simulation, and quantum metrology. Recent improvements in both fabrication techniques and qubit design have allowed the community to consider coupling large ensembles of artificial atoms, such as superconducting qubits, to a resonator. Here, we demonstrate the coherent coupling between a microwave resonator and a macroscopic ensemble composed of several thousand superconducting flux qubits, where we observe a large dispersive frequency shift in the spectrum of 250MHz. We achieve the large dispersive shift with a collective enhancement of the coupling strength between the resonator and qubits. These results represent the largest number of coupled superconducting qubits realized so far.

Controllable quantum dynamics of inhomogeneous nitrogen-vacancy center ensembles coupled to superconducting resonators.

We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.

Multiplexing Read-Out of Charge Qubits by a Superconducting Resonator**Supported by the National Basic Research Program of China under Grant No 2011CBA00200, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB01030000, and the National Natural Science Foundation of China under Grant Nos 11222438, 11174267, 61306150, 11304301 and 91421303.

Wavelength division multiplexing (WDM) is widely used in modern optics and electronics. For future quantum computers, the integration of readout is also vitally important. Here we incorporate an idea of WDM to demonstrate multiplexing readout of charge qubits by using a single integrated on-chip superconducting microwave resonator. Two distant qubits formed by two graphene double quantum dots (DQDs) are simultaneously readout by an interconnected superconducting resonator. This readout device is found to have 2 MHz bandwidth and charge sensitivity. Different frequency gate-modulations, which are used selectively to change the impedance of the qubits, are applied to different DQDs, which results in separated sidebands in the spectrum. These sidebands enable a multiplexing readout for the multi-qubits circuit. This architecture can largely reduce the amount of detectors and can improve the prospect for scaling-up of semiconductor qubits.

Development of a <sup>1</sup>H-<sup>13</sup>C Dual-Optimized NMR Probe Based on Double-Tuned High Temperature Superconducting Resonators

Nuclear magnetic resonance (NMR) spectroscopy is a very powerful technique to study molecular structure and dynamics because of the rich chemical information it can extract. However, low inherent sensitivity is the Achilles' heel of NMR. The use of high temperature superconducting (HTS) resonators as pick-up coils in NMR probes can significantly improve the detection sensitivity of NMR and expand the use of NMR for dilute and mass-limited samples. In previously proposed HTS-based probes, the resonators for the various channels are nested orthogonally around the sample region. With this configuration, optimal sensitivity can be achieved only by the single innermost channel, which has its coils closest to the sample. We report here a new configuration in which the NMR probe has been simultaneously optimized for detection sensitivity of two channels, namely, hydrogen and carbon. The probe employs novel double-tuned HTS resonators that generate strong, uniform, and mutually orthogonal magnetic fields at the hydrogen and carbon NMR frequencies. The resonator is designed for optimal magnetic field homogeneity and minimal electric field in the sample region. Design considerations for the resonators and probe performance in NMR tests are presented.

Electrodynamics of planar Archimedean spiral resonator

We present a theoretical and experimental study of electrodynamics of a planar spiral superconducting resonator of a finite length. The resonator is made in the form of a monofilar Archimedean spiral. By making use of a general model of inhomogeneous alternating current flowing along the resonator and specific boundary conditions on the surface of the strip, we obtain analytically the frequencies fn of resonances which can be excited in such system. We also calculate corresponding inhomogeneous RF current distributions ψn(r), where r is the coordinate across a spiral. We show that the resonant frequencies and current distributions are well described by simple relationships fn=f1n and ψn(r)≃ sin[πn(r/Re)2], where n=1,2... and Re is the external radius of the spiral. Our analysis of electrodynamic properties of spiral resonators' is in good agreement with direct numerical simulations and measurements made using specifically designed magnetic probe and laser scanning microscope.

Composite arrays of superconducting microstrip line resonators

A novel design of an array of half-wave superconductive microstrip resonators is described. The resonator is intended to be useful for electron spin resonance studies of thin film samples at cryogenic temperatures. It achieves a high quality factor, has a small mode-volume, and creates a uniform magnetic field in a plane above the resonator. The device is made of thin film Niobium on sapphire wafer and is tested with a static magnetic field. Variation of Q-factor versus the magnetic field's strength at different temperatures is reported and is in a good agreement with simulation when the loss due to the vortices is included. Also, the power-dependence response of the resonator is shown in experiments and is verified by capturing the nonlinearity associated with the surface impedance of the superconducting film into the circuit model of the device.

Observation of Autler–Townes effect in a dispersively dressed Jaynes–Cummings system

We report on the spectrum of a superconducting transmon device coupled to a planar superconducting resonator in the strong dispersive limit where discrete peaks, each corresponding to a different number of photons, are resolved. A thermal population of 5.474 GHz photons at an effective resonator temperature of T = 120 mK results in a weak n = 1 photon peak along with the n = 0 photon peak in the qubit spectrum in the absence of a coherent drive on the resonator. Two-tone spectroscopy using independent coupler and probe tones reveals an Autler–Townes splitting in the thermal n = 1 photon peak. The observed effect is explained accurately using the four lowest levels of the dispersively dressed qubit–resonator system and compared to results from numerical simulations of the steady-state master equation for the coupled system.

Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators

Structured plasmonic metamaterial devices offer the design flexibility to be size scaled for operation across the electromagnetic spectrum and are extremely attractive for generating electromagnetically induced transparency and slow-light behaviors via coupling of bright and dark subwavelength resonators. Here, we experimentally demonstrate a thermally active superconductor-metal coupled resonator based hybrid terahertz metamaterial on a sapphire substrate that shows tunable transparency and slow light behavior as the metamaterial chip is cooled below the high-temperature superconducting phase transition temperature. This hybrid metamaterial opens up the avenues for designing micro-sized active circuitry with switching, modulation, and “slowing down terahertz light” capabilities.

High-Temperature Superconducting Spiral Resonator for Metamaterial Applications

This work studies high-temperature superconducting spiral resonators as a viable candidate for realization of RF/microwave metamaterial atoms. The theory of superconducting spiral resonators is discussed in detail, including the mechanism of resonance, the origin of higher order modes, the analytical framework for their determination, the effects of coupling scheme, and the dependence of the resonance quality factor and insertion loss on the parity of the mode. All the aforementioned models are compared with the experimental data from a microfabricated YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-δ</sub> (YBCO) spiral resonator. Moreover, the evolution of the resonance characteristics for the fundamental mode with variation of the operating temperature and applied RF power is experimentally examined, and its implications for metamaterial applications are addressed.

Non-equilibrium superconductivity in quantum-sensing superconducting resonators

Low temperature microwave superconducting resonators (SRs) are attractive candidates for producing quantum-sensitive, arrayable energy or power detectors for astrophysical and other precision measurement applications. Their readout uses a microwave probe signal with quanta of energy well below the threshold for pair-breaking in the superconductor. We have calculated the non-equilibrium quasiparticle and phonon distributions generated by the photons of the probe signal of a resonator operating well below its superconducting transition temperature Tc as the absorbed probe power was changed using the coupled kinetic equations described by Chang and Scalapino. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from their thermal equilibrium value for typical readout powers. From the driven quasiparticle distribution functions, the driven quasiparticle number densities and lifetimes were calculated. An effective temperature to describe the driven quasiparticles was defined. The non-equilibrium lifetimes were compared to the distribution-averaged thermal lifetimes at the effective temperature and good agreement was found typically within a few per cent. We used the non-equilibrium quasiparticle distribution to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter S21 of the SR as a function of absorbed power were found. The non-equilibrium S21 cannot be accurately modeled by a thermal distribution even at its own elevated temperature, having a higher quality factor in all cases studied, although for low absorbed powers the two effective temperatures are similar. From the non-equilibrium lifetimes and number densities we determined the achievable noise equivalent power (NEP) of the resonator used as a power detector as a function of absorbed microwave power. Simpler expressions to evaluate the effective quasiparticle temperature as a function of absorbed power have also been derived. We conclude that multiple photon absorption from the microwave probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator at temperatures well below Tc.

Enlargement of the Field of View and Maintenance of a High Signal-to-Noise Ratio Using a Two-Element High-Tc Superconducting Array in a 3T MRI

This study examines the enlargement of the field of view (FOV) and the maintenance of a high signal-to-noise ratio (SNR) through the use of two high-temperature superconducting (HTS) resonators in a 3T MRI. Two Bi2Sr2Ca2Cu3Ox (Bi-2223) surface resonators, each of 4-cm diameter, were used in a 3T MRI. Professionally made copper resonators operate at 300 K, but each Bi-2223 resonator, operated at 77 K and demonstrated a 3.75 fold increase in SNR gain. For the same scanning time, the SNR of the images of a rat’s brain and back, obtained using two small Bi-2223 surface resonators, was higher than that obtained using a single 8-cm surface resonator.