Topological insulators (TIs) implemented in synthetic dimensions have recently emerged as an attractive platform to explore higher-dimensional topological phases in compact systems. Here, we present a two-dimensional TI within a single-ring resonator enabled by acousto-optic interactions and electro-optic modulation. In our system, the synthetic dimensions are represented by the range of discrete optical modes supported by the ring resonator and their azimuthal angular order. Gauge fields responsible for the topological order in the synthetic lattice are realized by an array of racetrack couplers coupled to the resonator. We reveal topological bulk and chiral edge bands in time-resolved absorption/transmission spectra, and we show that the proposed system can support reconfigurable and nonreciprocal frequency conversion controlled by the probe frequency detuning. Interestingly, we also show that realistic phase mismatch and disorder in acousto-optic scattering can enable an amorphous TI phase in synthetic space, demonstrating robust nonreciprocal frequency conversion in this regime.

中文翻译：

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基于光机械谐振器的两个合成维度的拓扑绝缘体

在合成维度中实现的拓扑绝缘体 (TI) 最近已成为探索紧凑系统中更高维度拓扑相的有吸引力的平台。在这里，我们在通过声光相互作用和电光调制实现的单环谐振器中展示了二维 TI。在我们的系统中，合成尺寸由环形谐振器支持的离散光学模式范围及其方位角顺序表示。负责合成晶格中拓扑顺序的规范场由耦合到谐振器的跑道耦合器阵列实现。我们在时间分辨吸收/透射光谱中揭示了拓扑体和手性边带，我们表明，所提出的系统可以支持由探头频率失谐控制的可重构和非互易频率转换。有趣的是，我们还表明，声光散射中的实际相位失配和无序可以在合成空间中实现非晶 TI 相位，证明在这种情况下具有强大的非互易频率转换。