Superconducting Microstrip Resonators Research Articles

Integrated and DC-powered superconducting microcomb

Frequency combs, specialized laser sources emitting multiple equidistant frequency lines, have revolutionized science and technology with unprecedented precision and versatility. Recently, integrated frequency combs are emerging as scalable solutions for on-chip photonics. Here, we demonstrate a fully integrated superconducting microcomb that is easy to manufacture, simple to operate, and consumes ultra-low power. Our turnkey apparatus comprises a basic nonlinear superconducting device, a Josephson junction, directly coupled to a superconducting microstrip resonator. We showcase coherent comb generation through self-started mode-locking. Therefore, comb emission is initiated solely by activating a DC bias source, with power consumption as low as tens of picowatts. The resulting comb spectrum resides in the microwave domain and spans multiple octaves. The linewidths of all comb lines can be narrowed down to 1 Hz through a unique coherent injection-locking technique. Our work represents a critical step towards fully integrated microwave photonics and offers the potential for integrated quantum processors.

Cavity and ground effects on a superconducting microstrip resonator

Superconducting planar-transmission-line resonators play an increasingly important role in applications such as astronomical detection and circuit quantum electrodynamics. When measuring the transmission response of an array of resonators, however, one often observes some spurious resonances besides the intrinsic ones. In this letter, the effect of the cavity accommodating a half-wavelength superconducting microstrip resonator is investigated. An attenuation pole associated with the intrinsic resonance of the half-wavelength resonator is clearly observed and found to be resulted from the mutual coupling between the microstrip resonator and the cavity. In addition, it is demonstrated that adding a superconducting ground layer for such a microstrip resonator can avoid the frequency shift owing to an ever-present thin air gap between the microstrip resonator and the cavity and can also improve the Q factor of the microstrip resonator.

Network modeling of non-ideal superconducting resonator circuits

We originally develop a network analysis method to study the non-ideal superconducting resonator circuits. We model the resonator device by a 3-block serial network, consisting of input feedline, resonator-coupler and output feedline. We show that the resonance curve will be modified if non-negligible discontinuity (reflection) exists at input or output side of the resonator. The extracted resonance parameters (such as coupling quality factor Qc) from only fitting the transmission deviate from their true values as originally defined in matched impedance conditions, and the deviation depends on a single parameter which includes all the non-ideal effects from the circuits. We prove that the internal quality factor Qi can be accurately extracted from the modified transmission curve by using a very simple graphical method. Our methods and results are quantitatively verified by both simulations and experiments on superconducting microstrip resonators. Comparing to the usual circuit analysis, our network analysis method is more intuitive and easier to understand. It can serve as a general tool to study the non-ideal superconducting resonator circuits.

Analysis of HTS circular patch antennas including radome effects

AbstractIn this paper, the resonant frequencies, quality factors and bandwidths of high Tc superconducting circular microstrip patches in the presence of a dielectric superstrate loading have been studied using Galerkin testing procedure in the Hankel transform domain. The exact Green's function of the grounded dielectric slab is used to derive an electric field integral equation for the unknown current distribution on the circular disc. Thus, surface waves, as well as space wave radiation, are included in the formulation. London's equations and the two-fluid model of Gorter and Casimir are used in the calculation of the complex surface impedance of the superconducting circular disc. Galerkin testing is used in the resolution of the electric field integral equation. Two solutions using two different basis sets to expand the unknown disk currents are developed. The first set of basis functions used is the complete set of transverse magnetic and transverse electric modes of a cylindrical cavity with magnetic side walls. The second set of basis functions used employ Chebyshev polynomials and enforce the current edge condition. The computed values for a wide range of variations of superstrate thickness and dielectric constant are compared with different theoretical and experimental values available in the open literature, showing close agreement. Results are showing that the superstrate parameters should always be kept into account in the design stage of the superconducting microstrip resonators.

Tunable superconducting microstrip resonators

We report on a simple yet versatile design for a tunable superconducting microstrip resonator. Niobium nitride is employed as the superconducting material and aluminum oxide, produced by atomic layer deposition, as the dielectric layer. We show that the high quality of the dielectric material allows to reach the internal quality factors in the order of Qi∼104 in the single photon regime. Qi rapidly increases with the number of photons in the resonator N and exceeds 105 for N∼10−50. A straightforward modification of the basic microstrip design allows to pass a current bias through the strip and to control its kinetic inductance. We achieve a frequency tuning δf=62 MHz around f0=2.4 GHz for a fundamental mode and δf=164 MHz for a third harmonic. This translates into a tuning parameter Qiδf/f0=150. The presented design can be incorporated into essentially any superconducting circuitry operating at temperatures below 2.5 K.

Superconducting microstrip resonator for pulsed ESR of thin films

This article describes a superconducting microstrip resonator operating at 9.5GHz (X-band) that is specially designed for pulsed ESR on thin films. A novel configuration consisting of an array of half-wave length microstrip transmission lines generates a uniform magnetic field over a 2-D region of 100×1000μm2 with field homogeneity better than 5×10-2. Using the device, we demonstrate strong coupling of the resonator to an electron spin ensemble and pulsed ESR on Si:P.

Magnetic field induced properties of type II superconducting microstrip resonators

The vortex effects of high temperature superconducting (HTS) microstrip resonators have been studied using the theoretical approach developed by Coffey and Clem (CC). A rectangular HTS strip resonator printed on sapphire substrate and subjected to a static magnetic field is considered, where the HTS strip is in the mixed state. An impedance type Green’s function is derived which connects the strip current to the electric field around the resonator, in the Fourier transformed domain. Galerkin’s procedure is used in the spectral domain to determine the resonant frequency and the unloaded Q value, both of which are computed for different applied fields, reduced temperatures and superconducting strip thicknesses. The results reveal considerable influence of applied field on resonant frequency and quality factor due to vortex motion, which should be considered when designing resonators which operate under external magnetic field.

Effect of LaAlO3 twin-domain topology on local dc and microwave properties of cuprate films

Different imaging modes of low temperature laser scanning microscopy (LTLSM) have been applied to probe local optical and superconducting properties, as well as the spatial variations in thermoelectric and electronic (both dc and rf) transport, in a YBa2Cu3O6.95/LaAlO3 (YBCO/LAO) superconducting microstrip resonator with micron-range resolution. Additionally, the local sources of microwave nonlinearity (NL) were mapped in two-dimensions simultaneously by using the LTLSM in two-tone rf intermodulation distortion contrast mode as a function of (x,y) position of the laser beam perturbation on the sample. The influence of the direction of individual twin-domain YBCO blocks on its NL properties was analyzed in detail. The result shows the direct spatial correlation between NL microwave and dc electronic transport properties of the YBCO film that are imposed by the underlying twin-domain topology of the LAO substrate. In these circumstances, the scale of local NL current densities JIM(x,y) in different areas of the YBCO microstrip quantitatively coincide with the scale of local critical current densities Jc(x,y) measured at the same positions.

Normalized IMD Spectra of High-T C and Low-T C Superconducting Resonators

Analyzing the results of the two-tone intermodulation distortion (IMD) measurements for the 2.3 GHz YBa2Cu3O7− x and GdBa2Cu3O7− x microstrip resonators we described the IMD spectra by the normalized values of P IMDn/P 0, where P IMDn is the output power of the n-th order IMD product and P 0 is that of the fundamental tone. The circulating power in the resonator was normalized by the power of the third-order intercept: P circ/P TOI. It was found, that the examined resonators exhibited the same dependence of P IMDn/P 0 versus P circ/P TOI and the same dependence of P IMDn/P 0 versus the change of the microwave surface resistance (ΔR S) at any measurement temperature. We reproduced these measurements for the indium microstrip resonators of the same geometry and obtained the same results. We conclude, that the nonlinear response of the superconducting microstrip resonators in the high power range is strongly affected by a geometry-dominated hf loss mechanism (likely the hf hysteretic losses due to magnetic flux penetration), which overshadows other nonlinear mechanisms related to the intrinsic material properties. This conclusion is in agreement with the results of the indium disk resonator measurements.

Microwave nonlinear resonance incorporating the helium heating effect in superconducting microstrip resonators

Nonlinear microwave phenomena in superconducting niobium–teflon microstrip resonators cooled by liquid helium are studied. Helium heating caused by the losses of microwave power in superconductor changes the resonant frequency because of the temperature dependence of helium permittivity. Manifestations of this thermal instability discover a new type of nonlinear phenomena including the generation of the monochromatic microwave pulses, generation of acoustic signals. The found nonlinear resonances are explained by thermally induced variations of the helium dielectric permittivity caused by the microwave power dissipated in superconductor, which enable incorporating the jump nonlinearity of a liquid–vapour phase transition in helium.

Microwave nonlinear effects in He-cooled superconducting microstrip resonators

Nonlinear phenomena in superconducting niobium microstrip-like resonators filled by liquid helium are studied in microwaves. The found nonlinear resonance is explained by thermally induced variations of the helium dielectric permittivity caused by the microwave power losses in superconductor. A number of interesting manifestations of this thermal instability have been observed including the parametric pulse generation of the monochromatic microwave signal, generation of acoustic pulses.

Full-wave modelling of nonlinear power dependence of high-Tc superconducting microstrip resonators

Efficient modelling of the nonlinear power dependence of microwave surface resistance and resonant frequency of a high-Tc superconducting microstrip resonator using the modified spectral domain method is presented. The accuracy of the analysis has been confirmed by experimental measurements.

Superconducting microstrip resonator on YSZ buffered silicon

For the purpose of comparison we have fabricated identical microstrip gap-coupled meanderline half-wave resonators using both 500 nm thick aluminum and 500 nm thick YBa 2Cu 3O 7 high temperature superconductor films on 50 Ω cm (1 0 0) silicon buffered with a 50 nm film of yittria stabilized zirconia. The YBa 2Cu 3O 7 films were crack-free and exhibited a zero resistance temperature of 82 K. Measured Q-values at 15 K for this resonator were 560, in good agreement with the literature value of 0.002 for the tan δ for this type of silicon at these temperatures. The aluminum structures did not exhibit any resonance whatsoever. Clearly there is a significant advantage in using YBa 2Cu 3O 7 films at low temperatures. Fabrication, measurement and materials characterization are presented and the implications of the result are discussed.

Increased quality factor in superconducting microstrip resonators by selective removal of the gold contact layer

We present measurements of the unloaded quality factor of superconducting microstrip resonators at 77 K and 3.86 GHz. The resonators were made of 0.3 μm thick YBa2Cu3O7 films with a transition temperature of 90 K on both sides of ceria-buffered 3 inch sapphire wafers. In particular, we investigated the effect of a 0.3 μm thick gold contact layer on the resonator performance. It was found that the gold layer decreases the quality factor by a factor of almost 5. This result is due to an additional microwave loss in the gold film which can be quantitatively described by the impedance transformation rules for transmission lines. On the basis of the quantitative analysis, we suggest a selective removal of the contact layer by appropriate patterning in order to eliminate the extra loss without deterioration of the low-ohmic galvanic contact to the microwave housing. The experimental results demonstrate the usefulness of the proposed method. Their comparison with the calculated surface current density in the ground plane shows that the contact layer has to be in an area where the current is zero. Furthermore, the results reveal that the surface current density distribution in the ground plane and microstrip depends on the microwave power.

Nonlinear microwave effects in superconducting microstrip resonators based on YBCO thin films

Linear microstrip resonators based on YBaCuO thin films made by RF magnetron sputtering on MgO substrates have been characterized with transmission microwave measurements as a function of temperature (from 10 K to T/sub c/) and the incident microwave power (from -30 to 10 dBm). The variation of the resonant frequency with temperature has been used to determine the intrinsic parameters (/spl lambda//sub 0/, T/sub c/) of the thin film using a fitting procedure and appropriate models. For low microwave powers (<-18 dBm), the variation of the quality factor, the insertion loss and the surface resistance do not exhibit any nonlinear effect. For higher microwave powers nonlinear effects appear and the variation of the quality factor has shown that they vary in a different way according to three temperature zones. Various theoretical models have been used to discuss the experimental results. These zones can be correlated to the temperature dependence of the surface resistance, in particular to grain boundaries resistance and to penetration of microwave Josephson vortices into the weak links. Moreover, the variation of the measured surface resistance as a function of the RF surface magnetic field is discussed considering different models.

Intermodulation measurements in Nb superconducting microstrip resonators

The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.

The Anomalous Unloaded Quality Factor Behavior of High T c Superconducting Microstrip Resonator in Weak dc Magnetic Field

This paper reports the anomalous behavior of unloaded quality factor (Qu) of high Tc superconducting (HTSC) microstrip resonator in weak dc magnetic field (Bdc). The Qu behavior increases with the elevated applied Bdc, but beyond the certain Bdc value, decreases linearly with Bdc. We speculate that this behavior may be caused by edge effect. The behavior is modeled both by the coupled-grain model accounting for a distribution of the grain dimension and Coffey-Clem model.

Anomalous microwave response of high-temperature superconducting thin-film microstrip resonator in weak dc magnetic fields

We have studied an anomalous microwave (mw) response of superconducting YBa 2Cu 3O 7− δ (YBCO) microstrip resonators in the presence of a weak dc magnetic field, H dc. The surface resistance ( R s) and reactance ( X s) show a correlated non-monotonic behavior as a function of H dc. R s and X s were found to initially decrease with elevated H dc and then increase after H dc reaches a crossover field, H c, which is independent of the amplitude and frequency of the input mw signal within the measurements. The frequency dependence of R s is almost linear at fixed H dc with different magnitudes (< H c, = H c and > H c). The impedance plane analysis demonstrates that r H, which is defined as the ratio of the change in R s( H dc) and that in X s( H dc), is about 0.6 at H dc< H c and 0.1 at H dc> H c. The H dc dependence of the surface impedance is qualitatively independent of the orientation of H dc.

Imaging of microwave intermodulation fields in a superconducting microstrip resonator

Nonlinearities give rise to intermodulation distortion in superconducting microwave devices and currently limit their use to low power applications. We have developed a cryogenic imaging technique to spatially resolve intermodulation distortion and used it to image an 8.2 GHz high temperature superconducting Tl2Ba2CaCu2O8 microwave resonator. The images reveal that the fundamental and intermodulation electric fields obey a fixed relation throughout the device. We note that further refinements of intermodulation theory in resonant devices may be required to fully describe the data.

Experimental observation and simulation of unusual microwave response for the superconducting microstrip resonator at small dc magnetic field

An unusual microwave response of the surface impedance Zs of high-Tc thin films at an applied small dc magnetic field (Bdc) at 77 K, namely a decrease of Zs, is observed with the microstrip resonator technique. The resonant frequency is 1.107 GHz. The direction of Bdc is parallel or perpendicular to the a-b plane. Bdc ranges from 0 to 200 G. It is found that the surface resistance (Rs) at Bdc parallel to the a-b plane first decreases with Bdc and then increases above a crossover field. The Rs behaviour for Bdc perpendicular to the a-b plane is the same but with a different crossover field. The two behaviours can be collapsed to one curve by scaling the crossover fields. The changes of surface reactance Xs correlated linearly with the changes of Rs in the ranges of Bdc. The ratios rH of changes of Rs and Xs (rH = Rs/ Xs) are 0.5 at Bdc less than the crossover field and 0.1 at Bdc greater than the crossover field. The measurements also show that the crossover field is independent of rf input power. A phenomenological model is also proposed to explain this unusual behaviour. By adjusting fitting parameters the computed results agree with the experimental results qualitatively.