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Recent advancements in quantum technologies and advanced detection experiments have underscored the pressing need for the detection of exceedingly weak signals within the microwave frequency spectrum. Addressing this challenge, the Josephson Traveling Wave Parametric Amplifier (JTWPA) has been proposed as a cryogenic front-end amplifier capable of approaching the quantum noise limit while providing a relevant bandwidth. This research is centered on a comprehensive numerical investigation of the JTWPA, without resorting to simplifications regarding the nonlinearity of the essential components. Specifically, this study focuses on a thorough examination of the system, characterized by coupled nonlinear differential equations representing all components of the device. Proper input and output signals at the device's boundaries are considered. The analysis of the output signals undergoing the parametric amplification process involves a detailed exploration of phase-space dynamics and Fourier spectral analysis of the output voltage. This study is conducted while considering the parameters ruling the response of the device under pump and signal excitations. In addition to the expected signal amplification, the findings reveal that the nonlinear nature of the system can give rise to unforeseen phenomena, depending on the system's operational conditions, which include: the generation of pump tone harmonics, modulation of the signal gain, and incommensurate frequency generation-effects that are not easily accommodated by simplistic linearized approaches, Comment: 5 pages, 4 figures, DARTWARS project - INFN (Italy)

Noise at the quantum limit over a broad bandwidth is a fundamental requirement for future cryogenic experiments for neutrino mass measurements, dark matter searches and Cosmic Microwave Background (CMB) measurements as well as for fast high-fidelity read-out of superconducting qubits. In the last years, Josephson Parametric Amplifiers (JPA) have demonstrated noise levels close to the quantum limit, but due to their narrow bandwidth, only few detectors or qubits per line can be read out in parallel. An alternative and innovative solution is based on superconducting parametric amplification exploiting the travelling-wave concept. Within the DARTWARS (Detector Array Readout with Travelling Wave AmplifieRS) project, we develop Kinetic Inductance Travelling-Wave Parametric Amplifiers (KI-TWPAs) for low temperature detectors and qubit read-out. KI-TWPAs are typically operated in a threewave mixing (3WM) mode and are characterised by a high gain, a high saturation power, a large amplification bandwidth and nearly quantum limited noise performance. The goal of the DARTWARS project is to optimise the KI-TWPA design, explore new materials, and investigate alternative fabrication processes in order to enhance the overall performance of the amplifier. In this contribution we present the advancements made by the DARTWARS collaboration to produce a working prototype of a KI-TWPA, from the fabrication to the characterisation.

Superconducting parametric amplifiers offer the capability to amplify feeble signals with extremely low levels of added noise, potentially reaching quantum-limited amplification. This characteristic makes them essential components in the realm of high-fidelity quantum computing and serves to propel advancements in the field of quantum sensing. In particular, Traveling-Wave Parametric Amplifiers (TWPAs) may be especially suitable for practical applications due to their multi-Gigahertz amplification bandwidth, a feature lacking in Josephson Parametric Amplifiers (JPAs), despite the latter being a more established technology. This paper presents recent developments of the DARTWARS (Detector Array Readout with Traveling Wave AmplifieRS) project, focusing on the latest prototypes of Kinetic Inductance TWPAs (KITWPAs). The project aims to develop a KITWPA capable of achieving $20\,$ dB of amplification. To enhance the production yield, the first prototypes were fabricated with half the length and expected gain of the final device. In this paper, we present the results of the characterization of one of the half-length prototypes. The measurements revealed an average amplification of approximately $9\,$dB across a $2\,$GHz bandwidth for a KITWPA spanning $17\,$mm in length.

A wide-bandwidth and low-noise amplification chain in the microwave regime is crucial for the efficient read-out of quantum systems based on superconducting detectors, such as Microwave Kinetic Inductance Detectors (MKIDs), Transition Edge Sensors (TESs), Magnetic Microcalorimeters (MMCs), and RF cavities, as well as qubits. Kinetic Inductance Travelling Wave Parametric Amplifiers (KI-TWPAs) operated in a three-wave mixing fashion have demonstrated exceptional dynamic range and low-noise performance, approaching the quantum limit. These amplifiers can be fabricated using a single layer of a high kinetic inductance film as weakly dispersive artificial transmission lines, with the ability to control the phase-matched bandwidth through dispersion engineering. In this study, we present the optimisation of the rf sputter-deposition process of NbTiN films using a Nb80%T20 target, with the goal of achieving precise control over film characteristics, resulting in high kinetic inductance while maintaining a high transition temperature. The parameter landscape related to the different sputtering conditions, such as pressure, power, and nitrogen flow, has been explored and the film thickness has been used as a fine-tuning parameter to adjust the properties of the final NbTiN films used for the fabrication of KI-TWPAs. As a final result, we have obtained a NbTiN film with a kinetic inductance of 8.5 pH/sq which we have exploited to fabricate KI-TWPA prototype devices, showing promising amplification performance.

Detection of low-reflectivity objects can be improved by the so-called quantum illumination procedure. However, quantum detection probability exponentially decays with the source bandwidth. The Josephson Parametric Amplifiers (JPAs) technology utilized as a source, generating a pair of entangled signals called two-mode squeezed vacuum states, shows a very narrow bandwidth limiting the operation of the microwave quantum radar (MQR). In this paper, for the first time, a microwave quantum radar setup based on quantum illumination protocol and using a Josephson Traveling Wave Parametric Amplifier (JTWPA) is proposed. Measurement results of the developed JTWPA, pumped at 12 GHz, show an ultrawide bandwidth equal to 10 GHz at X-band making our MQR a promising candidate for the detection of stealth objects.

In this paper, we propose a novel kind of Josephson-Energy Suppression Pump (JESP) controlled by a fully magnetic flux drive. The device presented here is composed of two superconducting loops interrupted at one side by superconducting nanowires which are joined together by a superconducting island. The phase difference developed at the edges of the nanowires by means of the magnetic flux threading the loops can collapse their Cooper condensates, leading to complete suppression of the Josephson energies. This mechanism allows to greatly reduce the leakage current when performing Cooper pair pumping by a pure magnetic pumping cycle without involving any gate modulation. The pumping capability of the JESP is studied through a master equation approach in the non-adiabatic case.

Detection of low-reflectivity objects can be enriched via the so-called quantum illumination procedure. In order that this quantum procedure outperforms classical detection protocols, entangled states of microwave radiation are initially required. In this paper, we discuss the role of Josephson Traveling Wave Parametric Amplifiers (JTWPAs), based on circuit-QED components, as suitable sources of a two-mode squeezed vacuum state, a special signal-idler entangled state. The obtained wide bandwidth makes the JTWPA an ideal candidate for generating quantum radiation in quantum metrology and information processing applications.

A quantum model for Josephson-based metamaterials working in the Three-Wave Mixing (3WM) and Four-Wave Mixing (4WM) regimes at the single-photon level is presented. The transmission line taken into account, namely Traveling Wave Josephson Parametric Amplifier (TWJPA), is a bipole composed by a chain of rf-SQUIDs which can be biased by a DC current or a magnetic field in order to activate the 3WM or 4WM nonlinearities. The model exploits a Hamiltonian approach to analytically determine the time evolution of the system both in the Heisenberg and interaction pictures. The former returns the analytic form of the gain of the amplifier, while the latter allows recovering the probability distributions vs. time of the photonic populations, for multimodal Fock and coherent input states. The dependence of the metamaterial's nonlinearities is presented in terms of circuit parameters in a lumped model framework while evaluating the effects of the experimental conditions on the model validity.

In the last few years, several groups have proposed and developed their own platforms demonstrating quantum-limited linear parametric amplification, with evident applications in quantum information and computation, electrical and optical metrology, radio astronomy and basic physics concerning axion detection. Here we propose a short review on the physics behind parametric amplification via metamaterials composed by coplanar wave-guides embedding several Josephson junctions. We present and compare different schemes that exploit the nonlinearity of the Josephson current-phase relation to mix the so-called signal, idler and pump tones. The chapter then presents and compares three different theoretical models, developed in the last few years, to predict the dynamics of these nonlinear systems in the particular case of a 4-Wave Mixing process and under the degenerate undepleted pump assumption. We will demonstrate that, under the same assumption, all the results are comparable in terms of amplification of the output fields.