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.
While designing the energy-momentum relation of photons is key to many linear, non-linear, and quantum optical phenomena, a new set of light-matter properties may be realized by employingthe topology of the photonic bath itself. In this work we investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically-induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects. Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel. More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations.
Chiral quantum optics has become a burgeoning field due to its potential applications in quantum networks or quantum simulation of many-body physics. Current implementations are basedon the interplay between local polarization and propagation direction of light in nanophotonic structures. In this manuscript, we propose an alternative platform based on coupling quantum emitters to a photonic \emph{sawtooth} lattice, a one-dimensional model with an effective flux per plaquette introduced by complex tunnelings. We study the dynamics emerging from such structured photonic bath and find the conditions to obtain quasi-perfect directional emission when the emitters are resonant with the band. In addition, we find that the photons in this bath can also mediate complex emitter-emitter interactions tunable in range and phase when the emitters transition frequencies lie within a band-gap. Since these effects do not rely on polarization they can be observed in platforms beyond nanophotonics such as matter-waves or circuit QED ones, of which we discuss a possible implementation.