Engineering the thin film characteristics for optimal performance of superconducting kinetic inductance amplifiers using a rigorous modelling technique

Abstract

Background: Kinetic Inductance Travelling Wave Parametric Amplifiers (KITWPAs) are a new variant of superconducting amplifier that can potentially achieve high gain with quantum-limited noise performance over broad bandwidth, which is important for many ultra-sensitive experiments. In this paper, we present a novel modelling technique that can better capture the electromagnetic behaviour of a KITWPA without the translation symmetry assumption, allowing us to flexibly explore the use of more complex transmission line structures and better predict their performance. Methods: In order to design a KITWPA with optimal performance, we investigate the use of different superconducting thin film materials, and compare their pros and cons in forming a high-gain low-loss medium feasible for amplification. We establish that if the film thickness can be controlled precisely, the material used has less impact on the performance of the device, as long as it is topologically defect-free and operating within its superconducting regime. With this insight, we propose the use of Titanium Nitride (TiN) film for our KITWPA as its critical temperature can be easily altered to suit our applications. We further investigate the topological effect of different commonly used superconducting transmission line structures with the TiN film, including the effect of various non-conducting materials required to form the amplifier. Results: Both of these comprehensive studies led us to two configurations of the KITWPA: 1) A low-loss 100 nm thick TiN coplanar waveguide amplifier, and 2) A compact 50 nm TiN inverted microstrip amplifier. We utilise the novel modelling technique described in the first part of the paper to explore and investigate the optimal design and operational setup required to achieve high gain with the broadest bandwidth for both KITWPAs, including the effect of loss. Conclusions: Finally, we conclude the paper with the actual layout and the predicted gain-bandwidth product of our KITWPAs.

Non-degenerate-pump four-wave mixing kinetic inductance travelling-wave parametric amplifiers

“…Performing the substitution results in a large number of cross-terms that requires a non-trivial amount of algebraic manipulation, which can be computed using an algebra manipulation software such as Mathematica. Collecting the relevant terms that oscillate at the same frequencies, and following the procedure described in [23,24], results in a set of four coupled differential equations, which are the generalised CMEs, where…”

“…Furthermore, harmonics of the pump tone are also generated in the non-linear medium, which require suppression in order to prevent shockwave formation [25] and to ensure maximum power transfer from the pump to the signal tone. Both of these effects would exist in a KITWPA regardless of the operational mode i.e., DP-4WM or DC-3WM, and can be suppressed via a technique called the dispersion engineering, where stopbands are created in the dispersion relation of the KITWPA by periodically modulating the impedance of the transmission line along its length with discretely loaded short sections [10,24,26,27].…”

“…To demonstrate the feasibility of this configuration, here we present a 6-12 GHz NP-4WM KITWPA design simulated using the procedure described in [24]. Figure 3 shows a drawing of the KITWPA design, which comprises an inverted microstrip transmission line comprising 650 unit cells to give a total transmission line length of 49.6mm.…”

“…With the placement of = f 6.148 GHz pumps on the leading edges of the first and second stopbands, respectively, we show that the pump harmonics and their cross-terms would fall into the subsequent stopbands at higher frequencies. The |S 21 | spectrum presented here has been simulated using the realistic modelling technique described in [24], which has been shown to accurately predict the measured performance of KITWPAs when the surface resistance of the superconducting film is calibrated to be close to negligible compared to the BCS prediction [28] at cryogenic temperature. Figure 5 .…”

Operation of kinetic-inductance travelling wave parametric amplifiers at millimetre wavelengths

“…Once we obtain the DC-biased transmission curve, it is straightforward to simulate the gain curve. Here, we use our coupled-mode equation (CME) model as presented in [17] but modified to operate in the DC3WM mode. As shown in figure 2, we successfully recover a gain curve that matches very well with the measurement, not only the level of gain but the bandwidth and the overall gain-bandwidth profile.…”