Tera-sample-per-second arbitrary waveform generation in a synthetic dimension

Synthetic dimension opens new horizons in quantum physics and topological photonics by enabling new dimensions for field and particle manipulations. The most appealing property of the photonic synthetic dimension is its ability to emulate high-dimensional optical behavior in a unitary physical system. Here we show that the photonic synthetic dimension can transform technical problems in photonic systems between dimensionalities, providing unexpected solutions to technical problems that are otherwise challenging. Specifically, we propose and experimentally demonstrate a fully reconfigurable photonic Galton board (PGB) in the temporal synthetic dimension, in which the temporal high-speed challenge is translated into a spatial fiber-optic length matching problem, leading to the generation of tera-sample-per-second arbitrary waveforms with ultimate flexibility. In the experiments, an arbitrary waveform with a widely tunable sampling rate, ranging from 10.42 GSa/s to a record high of 1.64 TSa/s, is demonstrated. The concept of dimension conversion offers possible solutions to various physical dimension-related problems, such as super-resolution imaging, high-resolution spectroscopy, and high-precision time measurement.