Controllable coupling between the odd and even fundamental modes of an asymmetric half-wavelength superconducting coplanar waveguide resonator is demonstrated. The resonant frequency of the even mode Ωe could be tuned by an external magnetic field, while the resonant frequency of the odd mode Ωo is field independent. To realize the tunability of Ωe, the central conductor of the NbN-based resonator was galvanically coupled to an array of Al-based rf-SQUIDs (radio frequency superconducting quantum interferometer device). These rf-SQUIDs are placed in only one resonator gap, ensuring its strong asymmetry. By adjusting the appropriate external magnetic flux Φ, equal frequencies of both modes were obtained. At this resonant point Ωo(Φ)=Ωe(Φ) an avoided level crossing of the eigenfrequencies was observed, demonstrating the coupling between the odd and even fundamental modes.

The high kinetic inductance of niobium nitride (NbN) thin films can be used for an implementation of compact on-chip inductances in cryoelectronic circuits. Here, for the first time, we demonstrate the implementation of a hybrid superconducting technology that includes the fabrication of standard aluminum submicron Josephson junctions and the NbN atomic layer deposition process. As an example, we fabricated and characterized a single and array of Al Josephson junctions together with NbN interconnections. The main Al Josephson junction parameters as well as NbN superconducting properties are in a good agreement with the values obtained by our standard fabrication process. The combination of technological processes for the NbN layers with Al Josephson junction allows implementing a new generation of innovative superconducting devices for different applications.

The operating principle of traveling-wave parametric amplifiers is typically understood in terms of the standard coupled mode theory, which describes the evolution of forward propagating waves without any reflections, i.e. for perfect impedance matching. However, in practice, superconducting microwave amplifiers are unmatched nonlinear finite-length devices, where the reflecting waves undergo complex parametric processes, not described by the standard coupled mode theory. Here, we present an analytical solution for the TWPA gain, which includes the interaction of reflected waves. These reflections result in corrections to the well-known results of the standard coupled mode theory, which are obtained for both 3-wave and 4-wave mixing processes. Due to these reflections, gain is enhanced and unwanted nonlinear phase modulations are suppressed. Predictions of the model are experimentally demonstrated on two types of unmatched TWPA, based on coplanar waveguides with a central wire consisting of i) a high kinetic inductance superconductor, and ii) an array of 2000 Josephson junctions.

Experimental search of galactic axions requires detection of single photons in the microwave range. We work on a novel approach to detect single microwave photons based on a coherent collective response of quantum states occurring in a superconducting qubit network (SQN) embedded in a low-dissipative superconducting resonator. We propose a two resonators detector configuration with two parallel resonators without common part and with separated input and output terminals. The device consists of a low-dissipative resonator with embedded SQN in which microwave photons arrive ("signal resonator"), and a transmission line for measuring the frequency dependent transmission coefficient demonstrating resonant drops at the qubit frequencies ("readout resonator"). In comparison with T-type three terminal device recently proposed and investigated by us, the device with two resonators with separated input and output terminals doesn't contain common part of both resonators and exclude an unwanted noise from measurement readout circuits to the signal resonator. A layout of two resonators four terminal SQN detectors containing 5 flux qubits weakly coupled to a low-dissipative signal and readout resonator was developed and optimized. The samples were fabricated by Manhattan Al-based technology with Nb resonator circuits. The SQN detector was experimentally tested in terms of microwave measurements of scattering parameters of both resonators and crosstalk properties. Comparison of experimental data with results of the simulations permits one to conclude that the electromagnetic conditions of the fundamental resonant peak of 8.5 GHz of both resonators aren't affected by the crosstalk phenomenon and their performances provided by the design remain not altered for correct device operation.

The major task of detecting axions or axion-like particles has two challenges. On the one hand, the ultimate sensitivity is required, down to the energy of a single microwave photon of the yoctojoule range. On the other hand, since the detected events are supposed to be rare, the dark count rate of the detector must be extremely low. We show that this trade-off can be approached due to the peculiar switching dynamics of an underdamped Josephson junction in the phase diffusion regime. The detection of a few photons’ energy at 10 GHz with dark count time above 10 s and the efficiency close to unity was demonstrated. Further enhancements require a detailed investigation of the junction switching dynamics.

The Josephson junction as a switching detector of weak signals is investigated in presence of noise in the frame of rotating pendulum model. The parameter range, where the detection can be more efficient, is found. It has been demonstrated, that with decrease of the signal power the double minima of the mean switching time and the standard deviation are transformed into a single minimum, which corresponds to interplay between noise suppression and resonant activation regimes. The resonant nature of escape allows to detect weak signals, whose amplitudes are weaker than the difference between critical cur-rent and bias current of a Josephson junction. With decrease of damping an efficient detection becomes possible even at subharmonics of the resonance frequency. (c) 2021 Elsevier Ltd. All rights reserved.

We present a blueprint for a maser with a single three-level transmon superconducting artificial atom. The system can be pumped coherently via a two-photon process, and to achieve high population inversion, the relaxation rate of the metastable state is increased via an auxiliary low-$Q$ cavity coupled to a transition between the transmon excited states. We show numerically that such a maser can operate both in the intermediate-coupling regime with super-Poissonian photon statistics and in the strong-coupling regime, where the statistics is sub-Poissonian. For the former the maser exhibits thresholdless behavior, and for the latter there is a well-defined pumping threshold. A useful side effect of the auxiliary resonator is that it allows to overcome the photon blockade effect for the pump, which would otherwise prevent a high photon population. Finally, we observe the bistability of the steady-state Wigner function and the self-quenching effect for some parameters.

We study the influence of a strong off-resonant driving signal to the energy levels of a superconducting flux qubit both experimentally and theoretically. In the experiment, we carry out a three-tone spectroscopy. This allows us to directly observe the modification of the qubit's energy levels by the dynamical Stark shift caused by the driving signal. A theoretical treatment including corrections from both, rotating and counter-rotating frame, allowed us to completely explain the observed experimental results and to reconstruct the influence of the strong driving to the dissipative dynamics as well as to the coupling constants of the qubit. As one potential application, the tunability of the minimal energy-level splitting of a superconducting qubit by a microwave induced dynamical Stark shift can help to overcome the parameter spread induced by the micro fabrication of superconducting artificial quantum circuits.

Microwave superconducting quantum circuits are strongly affected by various defects that are unavoidable during the production process. This paper presents a new method for measuring losses in an open transmission line. This line interacts through a capacitive coupling with a coplanar quarter-wavelength resonator, which is used to study losses therein. The authors have investigated the dependencies of losses on power and temperature (in the millikelvin range). It has been shown that major losses in a transmission line are due to the interaction of a microwave field with defects which are effectively described by two-level systems.

The demonstration of coherent quantum phase slips (CQPS) in disordered superconductors has opened up a new route towards exploring the fundamental charge–phase duality in superconductors, with the promise of devices with new functionalities and a robust quantum current standard based on CQPS. Here we demonstrate a device that integrates several CQPS junctions: the charge quantum interference device. The charge quantum interference device becomes the dual of the well-known superconducting quantum interference device, and is a manifestation of the Aharonov–Casher effect in a continuous superconducting system devoid of dielectric barriers.

This chapter is devoted to special realizations of lasing on single artificial atoms. It is demonstrated that special properties of quantum systems, implemented as an electrical circuit, may be explored to repeat original quantum optic experiments and extend them to new regimes. As we will discuss, this can, for example, lead to the realizations of lasing that only requires two states of the artificial atom. There we make use of the relaxation and of special coupling properties that naturally are achieved in the field of the circuit quantum electrodynamics.

Axions and axion-like particles appear in well-motivated extensions of the standard model of particle physics and may be the solution to the long-standing puzzle of the dark matter in our Universe. Several new experiments are foreseen in the next decade searching them in a wide range of the parameter space. In the mass region from few to several tens of microelectronvolt, detector sensitivity will be limited by the standard quantum limit of linear amplifiers and a new class of single microwave-photon detector will be needed. We have developed a single photon counter based on the voltage switching of an underdamped Josephson junction that is coupled to a coplanar waveguide. By measuring the switching voltage, we can register single photons at 14 GHz with the rate less than 1 photon per 3000 s.

We study the dynamics of a qubit-resonator system, when the r esonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consi der in terms of the qubit dressed states. Interaction of the dressed qubit with the second probing signal can essen tially change the amplitude of this signal. We calculate the transmission amplitude of the probe signal th rough the resonator as a function of the qubit’s energy and the driving frequency detuning. The regions of incr ease and attenuation of the transmitted signal are calculated and demonstrated graphically. We present the in fluence of the signal parameters on the value of the amplification, and discuss the values of the qubit-resonato r system parameters for an optimal amplification and attenuation of the weak probe signal.

Current-biased Josephson junctions are promising candidates for the detection of single photons in the microwave frequency domain. With modern fabrication technologies, the switching properties of the junction can be adjusted to achieve quantum limited sensitivity. Namely, the width of the switching current distribution can be reduced well below the current amplitude produced by a single photon trapped inside a superconducting cavity. However, for an effective detection a strong junction cavity coupling is required, providing nonlinear system dynamics. We compare experimental findings for our prototype device with a theoretical analysis aimed to describe the switching dynamics of junctions under microwave irradiation. Measurements are found in qualitative agreement with our simulations.

Quantum theory is expected to govern the electromagnetic properties of a quantum metamaterial, an artificially fabricated medium composed of many quantum objects acting as artificial atoms. Propagation of electromagnetic waves through such a medium is accompanied by excitations of intrinsic quantum transitions within individual meta-atoms and modes corresponding to the interactions between them. Here we demonstrate an experiment in which an array of double-loop type superconducting flux qubits is embedded into a microwave transmission line. We observe that in a broad frequency range the transmission coefficient through the metamaterial periodically depends on externally applied magnetic field. Field-controlled switching of the ground state of the meta-atoms induces a large suppression of the transmission. Moreover, the excitation of meta-atoms in the array leads to a large resonant enhancement of the transmission. We anticipate possible applications of the observed frequency-tunable transparency in superconducting quantum networks.

We construct a microwave detector based on the voltage switching of an underdamped Josephson junction that is positioned at a current antinode of lambda/4 coplanar waveguide resonator. By measuring the switching current and the transmission through a waveguide capacitively coupled to the resonator at different drive frequencies and temperatures, we are able to fully characterize the system and assess its detection efficiency and sensitivity. Testing the detector by applying a classical microwave field with the strength of a single photon yields a sensitivity parameter of 0.5, in qualitative agreement with theoretical calculations.

Technological processes for the fabrication of low- and high-Tc Josephson junctions, aimed for certain applications, are described. On the one hand, the integration of low-Tc superconductor digital electronics with superconducting sensor arrays enables input signal processing with quantum limited resolution at millikelvin temperatures. We describe this mixed signal superconductor technology for analogue sensor readout and signal multiplexing for operating temperatures down to 300 mK. On the other hand, by making use of modern high-Tc Josephson junction technology, sensitive magnetometers, which require a modest cooling power, can be developed. Examples of the application of the mentioned processes are shown.

We studied and optimised the properties of ultrathin superconducting niobium nitride films fabricated with a plasma-enhanced atomic layer deposition (PEALD) process. By adjusting process parameters, the chemical embedding of undesired oxygen into the films was minimised and a film structure consisting of mainly polycrystalline niobium nitride with a small fraction of amorphous niobium oxide and niobium oxo-nitrides were formed. For this composition a critical temperature of 13.8 K and critical current densities of 7 × 106 A cm–2 at 4.2 K were measured on 40 nm thick films. A fundamental correlation between these superconducting properties and the crystal lattice size of the cubic δ-niobium-nitride grains were found. Moreover, the film thickness variation between 40 and 2 nm exhibits a pronounced change of the electrical conductivity at room temperature and reveals a superconductor–insulator-transition in the vicinity of 3 nm film thickness at low temperatures. The thicker films with resistances up to 5 kΩ per square in the normal state turn to the superconducting one at low temperatures. The perfect thickness control and film homogeneity of the PEALD growth make such films extremely promising candidates for developing novel devices on the coherent quantum phase slip effect.

We present two possible methods for the fabrication of sub-micron sized Josephson junctions, namely the shadow-evaporation technique and the cross-type technology. Their importance for the field of modern super-conducting technology is discussed. As examples we present measurement results of a two-qubit sample and a prototype of a microwave detector fabricated each by one of the described methods. We review potential applications of superconducting quantum circuits based on the developed methods.

The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.