It is known that the quality factor (selectivity) of superconducting resonators is limited by the physical properties of the superconductor or by the quality of fabrication. It was previously shown that the selective properties of such resonators can be greatly improved by using harmonics of the input signal. The possibility of using nonlinear effects in superconductors to improve the tuning properties of superconducting resonators is considered. This possibility lies in regenerative operation of the resonator by operating it with single-circuit parametric amplification.
It is known that the quality factor (selectivity) of superconducting resonators is limited by the physical properties of the superconductor or by the quality of fabrication. It was previously shown that the selective properties of such resonators can be greatly improved by using harmonics of the input signal. The possibility of using nonlinear effects in superconductors to improve the tuning properties of superconducting resonators is considered. This possibility lies in regenerative operation of the resonator by operating it with single-circuit parametric amplification.
In this Master thesis, I present a theoretical description and experimental measurements of a tunable microwave resonator operated as a parametric amplifier. Superconducting parametric amplifiers have attracted great interest in recent years as it has been demonstrated that they can operate with a noise performance at the standard quantum limit. \nParametric amplification is achieved in the devices by modulating the electrical length of the resonator at twice the resonance frequency. The device measured in this thesis consists of a quarter-wavelength microwave resonator fabricated in a thin-film aluminum coplanar waveguide geometry. With a termination to ground through a Superconducting Quantum Interference Device (SQUID), the boundary condition of the resonator becomes sensitive to an applied magnetic field. This enables the tuning of the resonance frequencies, using a DC magnetic field, over a wide frequency range of 670MHz. Similarly, an AC magnetic field then allows for the modulation of the resonator electrical length at microwave frequencies. \nWe characterized the device by first measuring the DC tuning curves of the 2nd and 3rd harmonics of the resonator, around 4 GHz and 6 GHz respectively. We then studied parametric amplification in the device when the electrical length was modulated at approximately twice the resonance frequency of one of the modes. We scanned the pump frequency and pump power over a wide range to study the region in parameters which gives parametric gain. We performed an in-depth parameter sweep over this region, identifying pump parameters that provided maximum gain and maximum system noise improvements compared the following HEMT amplifier. \nWe find that the use of the parametric amplifier can improve the system noise temperature by more than 10 dB compared to a start-of-the-art commercial HEMT amplifier. This implies a performance near the standard quantum limit.
Abstract Superconducting resonators and parametric amplifiers are important components in scientific systems such as kinetic inductance detector arrays, frequency-domain multiplexers for other superconducting bolometers, spin-ensemble based memories, and circuit quantum electrodynamics demonstrators. In this paper, we report microwave measurements of superconducting Ti, Nb, and NbN resonators and their use as parametric amplifiers. These half-wave resonators were fabricated under near identical sputtering and lithographic conditions to ensure a like-for-like comparison of material properties. We report a wide range of properties and behaviours in terms of transition temperatures, resistivities, rate-limiting nonlinear response times, nonlinear dissipation, signs of the nonlinear inductances and their dependences on temperature and resonance harmonic. We have successfully operated Nb and NbN resonators as high gain parametric amplifiers, achieving greater than 20 dB of power amplification. We have shown that for a half-wave resonator, amplification can be realised not only in the fundamental resonance but also in the higher harmonic resonances. Further, for materials with high transition temperatures, e.g. Nb and NbN, amplification can be achieved at ∼ 4 K, i.e. a temperature maintained by a pulse tube cooler. Finally, in materials systems that have very fast response times, e.g. NbN, we have found that a cross-harmonic type of amplification can be achieved by placing pump tone in a different resonant mode as the signal and the idler. This wide range of observations will have important implications on the design and application of superconducting parametric amplifiers.
We present a formalism for modelling parametric amplification by resonators subject to rate-limited nonlinearity of mixed reactive/dissipative character, with particular relevance to superconducting devices. The non-linearity is assumed to be characterised by a single state parameter, which responds to changes in the energy stored in the resonator with finite response time. We show how the operating point and small signal amplification behaviour of the pumped resonator can be calculated, characterised and optimised in terms of a set of three dimensionless parameters. The formalism is then illustrated with a simple, first-order, model nonlinearity and the implications for amplification via quasiparticle generation in a superconductor discussed. Throughout we describe how the parameters needed to characterise the device can be determined experimentally from steady-state measurements. A key result of this paper is that rate-limiting of a nonlinear mechanism does not preclude amplification, although it does limit the bandwidth over which it may be achieved.
Nonlinear microwave resonators are a versatile tool in quantum information processing, enabling parametric amplification, continuous variable quantum computing, and engineered mode interactions. Many of these applications especially benefit from cubic nonlinearities enabling three-wave mixing; at the same time, they are limited by quartic nonlinearities giving rise to undesired Kerr effects. A recurrent challenge is therefore to engineer resonators with a finite cubic nonlinearity while suppressing quartic terms. Here, we investigate a superconducting resonator hosting two weak links fabricated from an aluminum-capped indium arsenide nanowire. We characterize the Kerr nonlinearity as a function of magnetic flux and gate bias, showing that it can be tuned to zero with either control parameter. Furthermore, we experimentally demonstrate three-wave mixing in a semiconductor-superconductor hybrid device, establishing nonzero cubic nonlinearity. An effective model based on Andreev bound states qualitatively captures the observed trends. Our results validate semiconductor-superconductor hybrid devices as a promising platform for tunable nonlinear superconducting circuits, with applications in parametric amplification, quantum control of bosonic modes, and engineering interactions between microwave modes.
Superconducting parametric amplifiers (SPAs) are critical components for ultralow-noise qubit readout in quantum computing, addressing the critical challenge of amplifying weak quantum signals without introducing noise that degrades coherence and computational fidelity. Unlike classical amplifiers, SPAs can achieve or closely approach quantum-limited performance, specifically the Standard Quantum Limit (SQL) of half a photon of added noise for phase-preserving amplification. The core principle of SPAs relies on parametric amplification, where energy is transferred from a strong pump tone to a weak input signal through non-dissipative nonlinear mixing processes. This is enabled by intrinsic nonlinearities in superconducting materials, primarily kinetic inductance in thin films (e.g., NbTiN, Al) and, more significantly, the Josephson effect in Josephson junctions. These nonlinear elements facilitate frequency mixing (three-wave or four-wave mixing) and can operate in phase-preserving or phase-sensitive amplification modes, with the latter allowing for noise squeezing below the SQL. This chapter emphasizes the significant role of resonator design in determining critical SPA performance metrics such as gain, bandwidth, and noise characteristics. It details both lumped-element (LC) and distributed-element (coplanar waveguide, CPW) resonators, discussing their unique properties, suitability for different frequency ranges, and the importance of achieving high-quality factors (Q) for efficient energy storage and minimal loss. A practical design and simulation of a meandered quarterwavelength CPW resonator coupled to a feed line is presented, illustrating how precise control over geometric parameters optimizes resonant frequency, coupling strength, and quality factor for high-fidelity qubit state discrimination.