Using a near-field microwave technique, two-dimensional images have been made of the second and third order intermodulation distortion (IMD) of Tl2Ba2CaCu2O8 and YBa2Cu3O7 thin film microwave resonators. It was found that second and third order IMD do not have identical spatial distributions, which indicates that physical mechanisms play different roles in their generation. This technique enables the investigation of the roles of these mechanisms. As an illustration, the sensitivity to magnetic fluxons of the two orders is described, with second order being more sensitive to fluxon density.
Oval-shaped resonance distortion as a signature of quasiparticle heating effect in a niobium superconducting resonator
School of Integrated Circuits, Tsinghua University（清华大学集成电路学院）；Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；Department of Astronomy, Tsinghua University（清华大学天文系）
Spatially-resolved techniques of laser scanning microscopy (LSM) have been used to image simultaneously the spatial variations of (i) rf current flow, J$_RF$(x,y), of (ii) areas of resistive dissipation and (iii) the sources of microwave nonlinearity (NL) in an operating superconducting resonator. The RF power dependent spatial evolution of these linear and NL microwave properties in the meander strip YBCO/LAO superconducting resonator have been LSM probed at different temperatures below Tc. The influence of both topologies of the twin-domain YBCO structure and of J$_RF$(x,y) peaks at the edge…
We report on the design and performance of a cryogenic (300 mK) near-field scanning microwave microscope. It uses a microwave resonator as the near-field sensor, operating at a frequency of 6 GHz and microwave probing amplitudes down to 100 uV, approaching low enough photon population (N~1000) of the resonator such that coherent quantum manipulation becomes feasible. The resonator is made out of a miniaturized distributed fractal superconducting circuit that is integrated with the probing tip, micromachined to be compact enough such that it can be mounted directly on a quartz tuning-fork, and …
Microwave resonators made from high-temperature superconducting (HTS) films are becoming increasingly commercially competitive in the market of modern communication technologies. However, unlike normal metals, the HTS device performance suffers from intrinsically nonlinear electrodynamics, resulting in harmonic generation and intermodulation (IM) distortion at all levels of circulating power. The dominant sources of IM response are believed to be inductive and localized in only small regions of the HTS film having the highest current densities J_RF(x,y). In our previous papers, examining micro…
Spatial scanning of the synchronously generated 2nd and 3rd order intermodulation distortion in superconducting resonators uncovers local nonlinearity hot spots, and possible time reversal symmetry breaking, using a simple probe fashioned from coaxial cable. It is clear that even and odd order nonlinearity in these samples do not share the same physical origins, as their temperature and static magnetic field dependences are quite different. 2nd order intermodulation distortion (IMD) remains strong in these measurements as the temperature continues to drop below TC to 77K even though the 3rd or…
We describe the use of a cryogenic near-field scanning microwave microscope to image microwave electric fields from superconducting and normal-metal microstrip resonators. The microscope employs an open-ended coaxial probe and operates from 77 to 300 K in the 0.01-20 GHz frequency range with a spatial resolution of about 200 mm. We describe the operation of the system and present microwave images of Cu and Tl2Ba2CaCu2O8 microstrip resonators, showing standing wave patterns at the fundamental and second harmonic frequencies.
We describe a practical design of an ultra-compact on-chip superconductive micro-resonator as a potential magnetic element of metamaterial. The achieved resonator size with respect to the wavelength in our experiment is about λ/ 14400. 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 counter-clockwise. We study the resonator spectral response and its inner modes using numerical simulation in HFSS. In experiment with a Laser Scanning Microscope (LSM) …
We investigate the microscopic origins of nonlinear rf response in superconducting electromagnetic resonators. Strong nonlinearity appearing in the transmission spectra at high input powers manifests itself through the emergence of jumplike features near the resonant frequency that evolve toward lower quality factor with higher insertion loss as the rf input power is increased. We directly relate these characteristics to the dynamics of localized normal regions (hot spots) caused by microscopic features in the superconducting material making up the resonator. A clear observation of hot-spot fo…
Superconducting microcircuits and metamaterials are promising candidates for use in new generation cryogenic electronics. Their functionality is largely justified by the macroscopic distribution of electromagnetic fields in arranged unit cells, rather than by the microscopic properties of composite materials. We present a new method for visualizing the spatial structure of penetrating microwaves with microscopic resolution in planar superconducting macroscopic resonators as the most important circuit-forming elements of modern microelectronics. This method uses a low-temperature laser scanning…
Intermodulation distortion (IMD) of microwave signals incident upon a superconducting YBa2Cu3O7 thin film sample on a LaAlO3 substrate is shown to relax as the sample magnetization also relaxes, revealing the signature of fluxon decay in the microwave distortion. The sample contained a microchannel of columnar defects that was introduced using heavy ion beam irradiation. After exposure to and then removal of a low strength static magnetic field, IMD relaxed due to thermal activation of fluxons over the surface barrier. This process influenced second and third order IMD differently, visible in …
We report a new technique of scanning capacitance microscopy at microwave frequencies. A near field scanning microwave microscope probe is kept at a constant height of about 1nm above the samplewith the help of Scanning Tunneling Microscope (STM) feedback. The microwaves are incident onto the sample through a coaxial resonator that is terminated at one end with a sharp tip (the same tip is used to conduct STM), and capacitively coupled to a feedback circuit and microwave source at the other end. The feedback circuit keeps the source locked onto the resonance frequency of the resonator and outp…
Superconducting thin film resonators employing strip geometries show great promise in rf/microwave applications due to their low loss and compact nature. However, their functionality is limited by nonlinear effects at elevated rf/microwave powers. Here, we show that by using a planar spiral geometry carrying parallel currents in adjacent turns, this limitation can be minimized. We investigate the rf current distributions in spiral resonators implemented with Nb thin films via laser scanning microscopy. The rf current density profile along the width of the individual turns of the resonators rev…
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 Li…
We have developed a scanning near-field microwave microscope that operates at cryogenic temperatures. Our system uses an open-ended coaxial probe with a 200 mm inner conductor diameter and operates from 77 to 300 K in the 0.01-20 GHz frequency range. In this paper, we present microwave images of the electric field distribution above a Tl2Ba2CaCu2O8 microstrip resonator at 77 K, measured at several heights. In addition, we describe the use of a frequency-following circuit to study the influence of the probe on the resonant frequency of the device.
Micro-channels of nanosized columnar tracks were planted by heavy-ion irradiation into superconducting microwave microstrip resonators that were patterned from YBa2Cu3O7-x thin films on LaAlO3 substrates. Three different ion fluences were used, producing different column densities, with each fluence having a successively greater impact on the nonlinearity of the device, as compared to a control sample. Photoresponse images made with a 638 nm rastered laser beam revealed that the channel is a location of enhanced photoresponse and a hot spot for the generation of intermodulation distortion. The…
The two tone intermodulation arising in MgB2 thin films deposited in-situ by planar magnetron sputtering on sapphire substrates is studied. Samples are characterised using an open-ended dielectric puck resonator operating at 8.8 GHz. The experimental results show that the third order products increase with the two-tone input power with a slope ranging between 1.5 and 2.3. The behaviour can be understood introducing a mechanism of vortex penetration in grain boundaries as the most plausible source of non linearities in these films. This assumption is confirmed by the analysis of the field depen…
We present a combined scanning force and tunneling microscope working in a dilution refrigerator that is optimized for the study of individual electronic nano-devices. This apparatus is equipped with commercial piezo-electric positioners enabling the displacement of a sample below the probe over several hundred microns at very low temperature, without excessive heating. Atomic force microscopy based on a tuning fork resonator probe is used for cryogenic precise alignment of the tip with an individual device. We demonstrate the local tunneling spectroscopy of a hybrid Josephson junction as a fu…
"The non-contact broadband transmission line flip-chip spectroscopy technique is utilized to probe resonances of mm-sized square kinetic planar resonators made from strongly disordered molybdenum carbide films, in the GHz frequency range. The temperature dependence of the resonances was analyzed by the complex conductivity of disordered superconductor, as proposed in Ref. arXiv:1407.2402 , which involves the Dynes superconducting density of states. The obtained Dynes broadening parameters relate reasonably to the ones estimated from scanning tunneling spectroscopy measurements. The eigenmodes …
We have used the LTLSM technique for a spatially resolved investigation of the microwave transport properties, nonlinearities and material inhomogeneities in an operating coplanar waveguide YBa_2Cu_3O_{7-δ} (YBCO) microwave resonator on an LaAlO_3 (LAO) substrate. The influence of twin-domain blocks, in-plane rotated grains, and micro-cracks in the YBCO film on the nonuniform rf current distribution were measured with a micrometer-scale spatial resolution. The impact of the peaked edge currents and rf field penetration into weak links on the linear device performance were studied as well. The …
A new phenomenological approach to spatially-resolved research of nonlinear (NL) microwave properties of operating thin-film superconducting resonators is proposed. The approach is based on frequency and spatial singularity of Laser Scanning Microscopy (LSM) images that can be extracted from a set of 2-D patterns representing x-y distribution of the LSM photoresponse, PR(x, y), at fixed third-order intermodulation (IMD) frequencies 2f1-f2 and 2f2-f1 as a result of two-tone resonator microwave excitation at equidistant frequencies f1 and f2 relative to the fundamental resonance, f0. It was show…
Superconducting metamaterials are a promising resource for quantum information science. In the context of circuit QED, they provide a means to engineer on-chip, novel dispersion relations and a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum reservoir engineering, and as an element for quantum simulation architectures. Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the for…
Diode Effect in Nonlinear High-Kinetic-Inductance Transmission Line Resonators
University of Ulm（乌尔姆大学）；Institute for Complex Quantum Systems and IQST, University of Ulm（乌尔姆大学复杂量子系统与IQST研究所）；German Aerospace Center (DLR), Institute of Quantum Technologies（德国航空航天中心（DLR）量子技术研究所）；Racah Institute of Physics, Hebrew University of Jerusalem（耶路撒冷希伯来大学拉卡物理研究所）；Qarakal Quantum Ltd.（Qarakal量子有限公司）
