We study the phenomena of topological amplification in one-dimensional traveling-wave parametric amplifiers. We find two phases of topological amplification, both with directional transportand exponential gain with the number of sites, and one of them featuring squeezing. We also find a topologically trivial phase with zero-energy modes which produces amplification but lacks topological protection. We characterize the resilience to disorder of the different phases, their stability, gain and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques.
Low-noise microwave amplification is crucial for detecting weak signals in quantum technologies and radio astronomy. An ideal device must amplify a broad range of frequencies whileadding minimal noise, and be directional, so that it favors the observer’s direction while protecting the source from its environment. Current amplifiers do not satisfy all these requirements, severely limiting the scalability of superconducting quantum devices. Here, we demonstrate the feasibility of building a near-ideal quantum amplifier using a homogeneous Josephson junction array and the non-trivial topology of its dynamics. Our design relies on breaking time-reversal symmetry via a non-local parametric drive, which induces directional amplification in a way similar to edge states in topological insulators. The system then acquires unprecedented amplifying properties, such as a gain growing exponentially with system size, exponential suppression of back-wards noise, and topological protection against disorder. We show that these features allow a state-of-the-art superconducting device to manifest near-quantum-limited directional amplification with a gain largely surpassing 20 dB and -30 dB of reverse attenuation over a large bandwidth of GHz. This opens the door for integrating near-ideal and compact pre-amplifiers on the same chip as quantum processors.