We study analytically and numerically the problem of two qubits with fixed coupling irradiated with quantum or classical fields. In the classical case, we derive an effective Hamiltonian, and construct composite pulse sequences leading to a CNOT gate. In the quantum case, we show that qubit-qubit-photon multiparticle entanglement and maximally entangled two-qubit state can be obtained by driving the system at very low powers (one quanta of excitation). Our results can be applied to a variety of systems of two superconducting qubits coupled to resonators.
We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together reveal different decay and decoherence mechanisms in a general microwave resonator. These results form a solid basis for understanding the scattering spectrums of networks of microwave resonators, and p…
We analyze the design of a potential replacement technology for the commercial ferrite circulators that are ubiquitous in contemporary quantum superconducting microwave experiments. The lossless, lumped element design is capable of being integrated on chip with other superconducting microwave devices, thus circumventing the many performance-limiting aspects of ferrite circulators. The design is based on the dynamic modulation of DC superconducting microwave quantum interference devices (SQUIDs) that function as nearly linear, tunable inductors. The connection to familiar ferrite-based circulat…
We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the elect…
We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, $\sqrt{\rm SWAP}$, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.
We describe the high fidelity dispersive measurement of a superconducting qubit using a microwave amplifier based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). The SLUG preamplifier achieves gain of 19 dB and yields a signal-to-noise ratio improvement of 9 dB over a state-of-the-art HEMT amplifier. We demonstrate a separation fidelity of 99% at 700 ns compared to 59% with the HEMT alone. The SLUG displays a large dynamic range, with an input saturation power corresponding to 700 photons in the readout cavity.
We report on a device that integrates eight superconducting transmon qubits in lambda/4 superconducting coplanar waveguide resonators fed from a common feedline. Using this multiplexing architecture, each resonator and qubit can be addressed individually thus reducing the required hardware resources and allowing their individual characterisation by spectroscopic methods. The measured device parameters agree with the designed values and the resonators and qubits exhibit excellent coherence properties and strong coupling, with the qubit relaxation rate dominated by the Purcell effect when brough…
Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.
We describe a microwave amplifier based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). The SLUG is embedded in a microstrip resonator, and the signal current is injected directly into the device loop. Measurements at 30 mK show gains of 25 dB at 3 GHz and 15 dB at 9 GHz. Amplifier performance is well described by a simple numerical model based on the Josephson junction phase dynamics. We expect optimized devices based on high critical current junctions to achieve gain greater than 15 dB, bandwidth of several hundred MHz, and added noise of order one quantum in the freque…
Superconducting current instability in thin rings, irradiated by a coherent microwave electromagnetic field, is studied. On the regular circular motion of the Cooper pairs in the supercurrent states the field imposes coherent oscillations of the condensate as a whole. The oscillating condensate should emit photons with the energies determined mainly by the discrete values of the superconducting ring energy. For the first time the probability of the supercurrent decay accompanied by the two- photon emission, is derived. The ring thickness is less than both the field skin-depth and the London pe…
We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multi-photon processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.
We discuss how to generate entangled coherent states of four \textrm{microwave} resonators \textrm{(a.k.a. cavities)} coupled by a superconducting qubit. We also show \textrm{that} a GHZ state of four superconducting qubits embedded in four different resonators \textrm{can be created with this scheme}. In principle, \textrm{the proposed method} can be extended to create an entangled coherent state of $n$ resonators and to prepare a Greenberger-Horne-Zeilinger (GHZ) state of $n$ qubits distributed over $n$ cavities in a quantum network. In addition, it is noted that four resonators coupled by a…
Nonequilibrium quasiparticles represent a significant source of decoherence in superconducting quantum circuits. Here we investigate the mechanism of quasiparticle poisoning in devices subjected to local quasiparticle injection. We find that quasiparticle poisoning is dominated by the propagation of pair-breaking phonons across the chip. We characterize the energy dependence of the timescale for quasiparticle poisoning. Finally, we observe that incorporation of extensive normal metal quasiparticle traps leads to a more than order of magnitude reduction in quasiparticle loss for a given injecte…
Microwave technology plays a central role in current wireless communications, standing among them mobile communication and local area networks (LANs). The microwave range shows relevant advantages with respect to other frequencies in open-air transmission, such as low absorption losses and low energy consumption, and it is additionally the natural working frequency in superconducting quantum technologies. Entanglement distribution between separate parties is at the core of secure quantum communications. Therefore, understanding its limitations in realistic open-air settings, specially in the r…
We investigate the quantum dynamics of a system of two coupled superconducting qubits under microwave irradiation. We find that, with the qubits operated at the charge co-degeneracy point, the quantum evolution of the system can be described by a new effective Hamiltonian which has the form of two coupled qubits with tunable coupling between them. This Hamiltonian can be used for experimental tests on macroscopic entanglement and for implementing quantum gates.
Current distribution for a thin superconducting strip shielded by two ideally conducting plains has been calculated. It is shown that at microwave requencies the current density has maximum over the center of the strip in contrast to the dc current pattern, which exhibits crowding over the edges.
We design and fabricate two types of superconducting niobium coplanar waveguide microwave resonators with different coupling capacitors on high purity Si substrates. Their microwave transmissions are measured at the temperatures of 20 mK. It is found that these two types of resonators possess significantly-different loaded quality factors; one is $5.6\times{10}^{3}$, and the other is $4.0\times{10}^{4}$. The measured data are fitted well by classical ABCD matrix approach. We found that the transmission peak deviates from the standard Lorentizian with a frequency broadening.
We investigate a coherent nonlinear feedback circuit constructed from pre-existing superconducting microwave devices. The network exhibits emergent bistable and astable states, and we demonstrate its operation as a latch and the frequency locking of its oscillations. While the network is tedious to model by hand, our observations agree quite well with the semiclassical dynamical model produced by a new software package [N. Tezak et al., arXiv:1111.3081v1] that systematically interpreted an idealized schematic of the system as a quantum optic feedback network.
Excitation of spin waves is considered in a superconducting ferromagnetic slab with the equilibrium magnetization both perpendicular and parallel to the surface. The surface impedance is calculated and its behavior near propagation thresholds is analyzed. Influence of non-zero magnetic induction at the surface is considered in various cases. The results provide a basis for investigation of materials with coexisting superconductivity and magnetism by microwave response measurements.
In a superconductor absorption of photons with an energy below the superconducting gap leads to redistribution of quasiparticles over energy and thus induces a strong non-equilibrium quasiparticle energy distribution. We have measured the electrodynamic response, quality factor and resonant frequency, of a superconducting aluminium microwave resonator as a function of microwave power and temperature. Below 200 mK, both the quality factor and resonant frequency decrease with increasing microwave power, consistent with the creation of excess quasiparticles due to microwave absorption. Counterint…
In this experimental study we show that the coupling between Nb/NbN superconducting microwave resonators and their feedline can be made amplitude dependent. We employ this mechanism to tune the resonators into critical coupling condition, a preferable mode of operation for a wide range of applications. Moreover we examine the dependence of critical coupling state on other parameters such as temperature and magnetic field. Possible novel applications based on such nonlinear coupling are briefly discussed.
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of incompatible observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental de…
We study the Bell's inequality violation by dynamical Casimir radiation with pseudospin measurement. We consider a circuit quantum electrodynamical set-up where a relativistically moving mirror is simulated by variable external magnetic flux in a SQUID terminating a superconducting-microwave waveguide. We analytically obtain expectation values of the Bell operator optimized with respect to channel orientations, in terms of the system parameters. We consider the effects of local noise in the microwave field modes, asymmetry between the field modes resulting from nonzero detuning, and signal los…
We experimentally and numerically study a NbN superconducting stripline resonator integrated with a microbridge. We find that the response of the system to monochromatic excitation exhibits intermittency, namely, noise-induced jumping between coexisting steady-state and limit-cycle responses. A theoretical model that assumes piecewise linear dynamics yields partial agreement with the experimental findings.
Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two …
We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device (SQUID). We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 μs when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on res…
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.
Non-resonant microwave absorption(NRMA) studies of superconducting MgB_2 at a frequency of 9.43 GHz in the field range -50 Gauss to 5000 Gauss are reported. The NRMA results indicate near absence of intergranular weak links. A linear temperature dependence of the lower critical field H_c1 is observed indicating a non s-wave superconductivity. However, the phase reversal of the NRMA signal which could suggest d-wave symmetry is also not observed.
We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positiv…
Microwave quantum memory promises advanced capabilities for noisy intermediate-scale superconducting quantum computers. Existing approaches to microwave quantum memory lack complete combination of high efficiency, long storage time, noiselessness and multi-qubit capacity. Here we report an efficient microwave broadband multimode quantum memory. The memory stores two spectral modes of single photon level microwave radiation in on-chip system of eight coplanar superconducting resonators. Single mode storage shows a power efficiency of up to $60\pm 3\%$ at single photon energy and more than $73\p…
We study photon assisted tunneling in Nb/AlOx/Nb Josephson junctions. A quantitative calibration of the microwave field in the junction allowed direct verification of the quantum efficiency of microwave photon detection by the junctions. We observe that voltages of photon assisted tunneling steps vary both with the microwave power and the tunneling current. However, this variation is not monotonous, but staircase-like. The phenomenon is caused by mutual locking of positive and negative step series. A similar locking is observed with Shapiro steps. As a result the superconducting gap assumes qu…
The temperature dependences of the enhanced critical current in wide and thin Sn films exposed to the microwave field have been investigated experimentally and analyzed. It was found that the microwave field stabilizes the current state of a wide film with respect to the entry of Abrikosov vortices. The stabilizing effect of irradiation increases with frequency. Using similarity between the effects of microwave enhancement of superconductivity observed for homogeneous (narrow films) and inhomogeneous (wide films) distributions of the superconducting current over the film width, we have succeed…
While the electrodynamic treatment of a superconducting thin film by Yeh et al. [Phys. Rev. B 48, 9861 (1993)] ostensibly has application for the "thin-film limit," their work is shown to employ bulk-like instead of thin-film electrodynamics, and as such obtains an ostensible violation of the first law of thermodynamics and a surface resistance independent of the resistivity. Other theoretical and experimental difficulties are briefly noted.
We discuss experimental results obtained using a tunable cylindrical coaxial cavity constituted by an outer Cu cylinder and an inner Pb-BSCCO wire. We have used this device for investigating the microwave response of the superconducting wire, both in the linear and nonlinear regimes. In particular, by tuning the different modes of the cavity to make them resonant at exactly harmonic frequencies, we have detected the power emitted by the superconducting inner wire at the second- and third-harmonic frequency of the driving field. The results obtained in the nonlinear regime, whether for the micr…
We investigated the microwave conductivity spectrum of FeSe$_{0.5}$Te$_{0.5}$ epitaxial films on CaF$_2$ in the vicinity of the superconducting transition. We observed the critical behavior of the superconducting fluctuations in these films with a dimensional crossover from two-dimensional to three-dimensional as the film thickness increased. From the temperature dependence of the scaling parameters we conclude that the universality class of the superconducting transition in FeSe$_{0.5}$Te$_{0.5}$ is that of the 3D-XY model. The lower limit of the onset temperature of the superconducting fluct…
We present an analytical and comprehensive description of the quantum dynamics of a microwave resonantly driven superconducting phase qubit coupled to a microscopic two-level system (TLS), covering a wide range of the external microwave field strength. Our model predicts several interesting phenomena in such an ac driven four-level bipartite system including anomalous Rabi oscillations, high-contrast beatings of Rabi oscillations, and extraordinary two-photon transitions. Our experimental results in a coupled qubit-TLS system agree quantitatively very well with the predictions of the theoretic…
We demonstrate theoretically that shining light on superconducting proximity structures controls the minigap and triplet proximity effect in normal and magnetic metals, respectively. Considering both a bilayer and Josephson junction geometry, we show that microwave irradiation with frequency $ω$ qualitatively alters the spectral properties of the system, controlling the minigap size $E_\text{mg}$ and even replacing the minigap with a strong peak of quasiparticle accumulation at zero energy when $ω=E_\text{mg}$. The interaction between light and Cooper pairs may thus open a route to active cont…
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.
In this paper we report some extraordinary nonlinear dynamics measured in the resonance curve of NbN superconducting stripline microwave resonators. Among the nonlinearities observed: aburpt bifurcations in the resonance response at relatively low input powers, asymmetric resonances, multiple jumps within the resonance band, resonance frequency drift, frequency hysteresis, hysteresis loops changing direction and critical coupling phenomenon. Weak links in the NbN grain structure are hypothesized as the source of the nonlinearities.
We demonstrate the operation of superconducting coplanar microwave resonators in a very large frequency range up to 50 GHz. The resonators are fabricated from niobium thin films on sapphire substrates and optimized for these high frequencies by small chip sizes. We study numerous harmonics of the resonators at temperatures between 1.5 K and 6 K, and we determine quality factors of up to 25000 at 1.5 K. As an example for spectroscopy applications of such resonators we detect the superconducting transition of a bulk tin sample at multiple probing frequencies.
Non-dissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, so-called Andreev bound states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a supercon…
The dynamics of a superconducting quantum point contact biased at subgap voltages is shown to be strongly affected by a microwave electromagnetic field. Interference among a sequence of temporally localized, microwave-induced Landau-Zener transitions between current carrying Andreev levels results in energy absorption and in an increase of the subgap current by several orders of magnitude. The contact is an interferometer in the sense that the current is an oscillatory function of the inverse bias voltage. Possible applications to Andreev-level spectroscopy and microwave detection are discusse…
We consider a two-band superconductor with relative phase $π$ between the two order parameters as a model for the superconducting state in ferropnictides. Within this model we calculate the microwave response and the NMR relaxation rate. The influence of intra- and interband impurity scattering beyond the Born and unitary limits is taken into account. We show that, depending on the scattering rate, various types of power law temperature dependencies of the magnetic field penetration depth and the NMR relaxation rate at low temperatures may take place.
When a thin-film ring with supercurrent is irradiated by coherent microwave field, the field induces coherent oscillations of all the Cooper pairs involved in the supercurrent. The oscillating charged condensate will emit photons with energies determined by the difference of quantized energy levels of the superconducting ring. This effect can be observed only in the rings, the thickness of which is less than both the field skin-depth and the London penetration depth. The probability of the microwave field-induced single-photon and two-photon emission is calculated. The energy - angle distribut…
We report a technique for applying a dc voltage or current bias to the center conductor of a high-quality factor superconducting microwave cavity without significantly disturbing selected cavity modes. This is accomplished by incorporating dc bias lines into the cavity at specific locations. The measured S-matrix parameters of the system are in good agreement with theoretical predictions and simulations. We find that at 4 K the quality factor of the cavity degrades by less than 1% under the application of a dc bias.
The surface impedance of Nb/CuMn (superconducting/spin-glass) bilayers has been measured at 10 GHz with the parallel plate resonator technique to obtain information about the exotic behavior of the order parameter in superconducting/magnetic proximity systems. The data strongly differs from the superconducting/normal-metal case, showing the magnetic nature of the CuMn layer, which acts as a weak ferromagnet. The results are described in the framework of two models for the electrodynamics of superconducting/ferromagnetic (S/M) bilayers characterized by a proximity-coupling length scale which is…
We briefly review some non-accelerator high-frequency applications of superconductors. These include the use of high-Tc superconductors in front-end band-pass filters in cellular telephone base stations, the High Temperature Superconductor Space Experiment, and high-speed digital electronics. We also present an overview of our work on a novel form of near-field scanning microscopy at microwave frequencies. This form of microscopy can be used to investigate the microwave properties of metals and dielectrics on length scales as small as 1 mm. With this microscope we have demonstrated quantitativ…
Precision measurements of the microwave surface resistance $R_{s}$ of in situ $MgB_{2}$ films directly reveal an exponential behavior of $R_{s}$ at low temperature indicating a fully-gapped order parameter. The entire temperature dependence of $R_{s}$ is well described by a Mattis-Bardeen formalism but with a small gap ratio of $Δ(0)/kT_{c}=0.72$, corresponding to $Δ(0)=1.9meV$.
We develop an explicitly gauge-invariant semiclassical approach to investigate nonlinear response of superconductors to monochromatic THz radiation. We demonstrate that in clean superconductors charge conservation forbids non-linear response to a uniform field. We apply our approach to quasi-two-dimensional films and obtain an explicit expression for the photoinduced current. We find that the photoinduced current exhibits a strong dependence on polarization and incidence angle of the radiation. Our predictions may be directly verified in experiments with quasi-two-dimensional superconducting f…
Vortices in superconductors driven at microwave frequencies exhibit a response related to the interplay between the vortex viscosity, pinning strength, and flux creep effects. At the same time, the trapping of vortices in superconducting microwave resonant circuits contributes excess loss and can result in substantial reductions in the quality factor. Thus, understanding the microwave vortex response in superconducting thin films is important for the design of such circuits, including superconducting qubits and photon detectors, which are typically operated in small, but non-zero, magnetic fie…
Measurements of the $10GHz$ microwave surface resistance of dense $MgB_{2}$ wire and pellet are reported. Significant improvements are observed in the wire with reduction of porosity. The data lie substantially above the theoretical estimates for a pure BCS s-wave superconductor . However the $R_{s}(20K)$ of the wire is an order of magnitude lower than that of polycrystal $YBa_{2}Cu_{3}O_{6.95}$ and matches with single crystal $YBa_{2}Cu_{3}O_{6.95}.$The results show promise for the use of $MgB_{2}$ in microwave applications.
The inelastic magnetic scattering of neutrons from thin superconducting films irradiated with microwave radiations, is analyzed. This process is due to the interaction of the magnetic field generated by the neutron, with the oscillating current induced by the electromagnetic field penetrated into the film. In the Born approximation, the neutron energy can both increase and decrease by the energy quantum of the field. The scattering cross section, which increases with decreasing the field frequency, is derived, and its numerical calculations are carried out. Measurements of this cross section g…
We have performed susceptibility, thermopower, dc resistance and microwave measurements on RuSr2EuCu2O8. This compound has recently been shown to display the coexistence of both superconducting and magnetic order. We find clear evidence of changes in the dc and microwave resistance near the magnetic ordering temperature (132 K). The intergranular effects were separated from the intragranular effects by performing microwave measurements on a sintered ceramic sample as well as on a powder sample dispersed in an epoxy resin. We show that the data can be interpreted in terms of the normal-state re…
The anomalous decrease in microwave surface resistance, R_{s}, of superconducting YBa_{2}Cu_{3}O_{7-d} (YBCO) thin films in the presence of a low dc magnetic field is studied using a microstrip resonator technique. We have done a dc field hysteresis measurement of R_{s} to study the effects of vortex penetration on the anomalous effect. It is shown that the anomaly happens at a field level far below the low critical field, H_{c1,strip}, of the superconducting microstrip and vortex (Abrikosov) penetration would eliminate the anomalous effect observed at low field. This implies that the anomalou…
We propose and demonstrate a spatial partition method for the high-frequency photo-response of superconducting devices correlated with inductive and resistive changes in microwave impedance. Using a laser scanning microscope, we show that resistive losses are mainly produced by local defects at microstrip edges and by intergrain weak links in the high-temperature superconducting material. These defects initiate nonlinear high-frequency response due to overcritical current densities and entry of vortices.
Microwave resonators with high quality factors have enabled many recent breakthroughs with superconducting qubits and photon detectors, typically operated in shielded environments to reduce the ambient magnetic field. Insufficient shielding or pulsed control fields can introduce vortices, leading to reduced quality factors, although increased pinning can mitigate this effect. A narrow slot etched into the resonator surface provides a straightforward method for pinning enhancement without otherwise affecting the resonator. Resonators patterned with such a slot exhibited over an order of magnitu…
We report the measurement of intermodulation gain in NbN superconducting stripline resonators. In the intermodulation measurements we inject two unequal tones into the oscillator, the pump and signal, both lying within the resonance band. At the onset of instability of the reflected pump we obtain a simultaneous gain of both the idler and the reflected signal. The measured gain in both cases can be as high as 15 dB, whereas to the best of our knowledge intermodulation gain greater than unity in superconducting resonators has not been reported before in the scientific literature.
We present a dual cut-off, dc-tunable low-pass microwave filter on a superconducting Nb microstrip with uniaxial asymmetric nanogrooves. The frequency response of the device was measured in the range $300$\,KHz to $14$\,GHz at different temperatures, magnetic fields, and dc current values. The microwave loss is most effectively reduced when the Abrikosov vortex lattice spatially matches the underlying washboard pinning landscape. The forward transmission coefficient $S_{21}(f)$ of the microstrip has a dc-tunable cut-off frequency $f_d$ which notably changes under dc bias reversal, due to the t…
