Driving a Josephson Traveling Wave Parametric Amplifier into chaos: Effects of a non-sinusoidal current–phase relation

We tackled the numerical analysis of the dynamic response of a Josephson Traveling Wave Parametric Amplifier (JTWPA) by varying the driving parameters, with a focus on the pathways leading to chaotic behavior. By tuning the working conditions, we explore the broad spectrum of dynamical regimes accessible to JTWPAs, delineating the conditions under which transition to chaos occurs. Furthermore, we extend our investigation to junctions characterized by a non-sinusoidal current phase relation (CPR) and explore the consequences on the amplifier's performance. Through the study of gain characteristics, Poincaré sections, and Fourier spectra, we provide an in-depth understanding of how CPR nonlinearity and nonsinusoidality influence the operational effectiveness and stability of JTWPAs. This investigation offers insights into optimizing the device for enhanced performance and robustness against chaotic disruptions, in order to establish a framework for predicting and controlling JTWPA behavior in practical applications. In fact, we identify the regions in the parameter space where the input signal is maximally amplified without excessive noise or undesired harmonics. This effort paves the way for the development of devices with tailored dynamic responses and for advancements in quantum computing and precision measurement technologies, where stability and high fidelity are of paramount importance.