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arXiv:2306.00685 · Superconductor Science and Technology

Nonlinear characteristics of Ti, Nb, and NbN superconducting resonators for parametric amplifiers

Songyuan Zhao, S. Withington, Christopher N. Thomas

Published Aug 16, 2023• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6668/acf0f1

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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.
Abstract Superconducting resonator parametric amplifiers are potentially important components for a wide variety of fundamental physics experiments and utilitarian applications. We propose and realise an operating scheme that achieves amplification through the use of non-degenerate pumps, which addresses two key challenges in the design of parametric amplifiers: non-continuous gain across the amplification band and pump tone removal. We have experimentally demonstrated the non-degenerate pumping scheme using a half-wave resonator amplifier based on NbN thin-film, and measured a peak gain of 26 dB and 3-dB bandwidth of 0.5 MHz. The two non-degenerate pump tones were positioned ∼10\sim 10∼10 ∼ 10 bandwidths above and below the frequency at which peak gain occurs. We have found the non-degenerate pumping scheme to be more stable compared to the usual degenerate pumping scheme in terms of gain drift over time, by a factor of 4. This scheme also retains the usual flexibility of NbN resonator parametric amplifiers in terms of reliable amplification in a ∼4\sim 4∼4 ∼ 4 K environment, and is suitable for cross-harmonic amplification. The use of pump tones at different frequencies allows phase-sensitive amplification when the signal tone is degenerate with the idler tone. A gain of 23 dB and squeezing ratio of 6 dB were measured.
Abstract The underlying nonlinear mechanisms behind the operation of travelling-wave parametric amplifiers (TWPAs) are important in determining their performance in terms of added noise, maximum gain, and bandwidth. We describe a method of characterising the underlying nonlinearity of a superconducting material in terms of its dissipative-reactive ratio and the response time of the underlying microscopic processes. We describe and calculate the different behaviour arising from the equilibrium supercurrent nonlinearity, which has low dissipation and fast response time, and the non-equilibrium heating nonlinearity, which has high dissipation and slow response time. We have fabricated TWPAs based on Al and Ti, and characterised their nonlinearities using our analysis. For both Al and Ti, the measured dissipative-reactive ratios and response times are quantitatively similar to predictions for the non-equilibrium heating nonlinearity. We were able to obtain more than 20 d B of peak power gain, although only over a narrow bandwidth of a few kilohertz. Our method of characterising the underlying nonlinearities could also be useful in the understanding and design of other superconducting nonlinear devices such as parametric up-converters, kinetic inductance Fourier transform spectrometers, and resonator parametric amplifiers.
Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.
Abstract Superconducting resonator parametric amplifiers achieve ultra-low-noise amplification through the nonlinear kinetic inductance of thin-film superconductors. One of the main challenges to the operation of these devices is the separation of the strong pump tone from the signal tone after amplification has been achieved. In this paper, we propose and experimentally demonstrate a pump separation method based on operating a half-wave superconducting resonator amplifier behind a cryogenic circulator. Our pump separation scheme does not involve post-amplification interference, and thereby avoids the delicate phase matching of two different pump paths. We demonstrate the scheme using two-port half-wave resonator amplifiers based on superconducting NbN thin-films. We present measurements of gain profiles and degrees of pump separation for amplifiers having different coupling quality factors. On an amplifier having a coupling quality factor of ∼2000, we measured a peak signal gain of 15 dB whilst achieving pump separation of 12 dB . The amplifier was stable for continuous measurements, and the gain drift was measured to be 0.15 dB over an hour. The same amplifier was operated at 3.2 K and achieved a peak signal gain of 11 dB whilst having a pump separation factor of 10.5 dB . The pump separation scheme, and these promising results, will advance the development of superconducting resonator amplifiers as an important technology in quantum sensing.
The nonlinear response associated with the current dependence of the superconducting kinetic inductance was studied in capacitively shunted NbTiN microstrip transmission lines. It was found that the inductance per unit length of one microstrip line could be changed by up to 20% by applying a dc current, corresponding to a single-pass time delay of 0.7 ns. To investigate nonlinear dissipation, Bragg reflectors were placed on either end of a section of this type of transmission line, creating resonances over a range of frequencies. From the change in the resonance linewidth and amplitude with dc current, the ratio of the reactive to the dissipative response of the line was found to be 788. The low dissipation makes these transmission lines suitable for a number of applications that are microwave- and millimeter-wave band analogs of nonlinear optical processes. As an example, by applying a millimeter-wave pump tone, very-wide-band parametric amplification was observed between about 3 and 34 GHz. Use as a current variable delay line for an on-chip millimeter-wave Fourier transform spectrometer is also considered.
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.