Self-phase-matched broadband amplification with a left-handed Josephson transmission line

Josephson traveling-wave parametric amplifiers (JTWPAs) are promising platforms for realizing broadband quantum-limited amplification of microwave signals. However, substantial gain in such systems is attainable only when strict constraints on phase matching of the signal, idler, and pump waves are satisfied---this is rendered particularly challenging in the presence of nonlinear effects, such as self- and cross-phase modulation, which scale with the intensity of propagating signals. In this work, we present a simple JTWPA based on ``left-handed'' (negative-index) nonlinear Josephson metamaterial, which has phase matching native to its design, precluding the need for any complicated circuit or dispersion engineering. The resultant efficiency of the four-wave-mixing process can implement gains in excess of 20 dB over few-gigahertz bandwidths with much shorter lines than previous implementations. Furthermore, the intrinsic phase matching considerably simplifies the JTWPA design and operation compared to the previous implementations based on ``right-handed'' (positive-index) Josephson metamaterials, making the proposed architecture particularly appealing for integration with large superconducting architectures. The left-handed Josephson transmission line introduced here constitutes an alternative modality in distributed Josephson circuits, and forms a crucial piece of the unified framework that can be used to inform the optimal design and operation of broadband microwave amplifiers.