Driven-dissipative topological phases in parametric resonator arrays

Álvaro Gómez-León, Tomás Ramos, Alejandro González-Tudela, and Diego Porras

Instituto de Física Fundamental (IFF), CSIC, Calle Serrano 113b, 28006 Madrid, Spain.

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Abstract

We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and 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 the robust topological protection of the others. We characterize the resilience to disorder of the different phases and their stability, gain, and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques.

Amplifiers are fundamental tools in today’s technology. Their uses range from quantum computation to astronomical and NMR devices, and their usefulness requires several properties to be fulfilled. For example, large gain allows to amplify weak signals fast, wide frequency bandwidth allows to maximize the range of applications, and low noise allows to separate the signals of interest from the background fluctuations.
For this reason, it is important to investigate new approaches to build amplifiers which can overcome those already existing.
In this work we have explored the phenomena of amplification in parametric resonator arrays.
We have shown that it is useful to harness ideas from topological systems and combine them with those of dissipative ones. In particular regimes, this leads to phases of topological amplification where one finds large directional gain, quantum-limited noise and broad bandwidth. In addition, amplification is topologically protected to perturbations and the steady-state can be used to generate squeezed states. Our results also provide a way to test new dissipative topological phases, where in contrast with the well-known case of the quantum Hall effect, now photons populate the system and their interaction with the environment is fundamental for their existence.
These types of topological amplifiers can be fabricated in several platforms, such as Josephson junctions, nano-mechanical oscillators and trapped ions. This means that their use can be widespread, and that their realization will also tackle fundamental questions about the physics of dissipative topological phases.

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