Quantized nonlinear Thouless pumping
Quantized nonlinear Thouless pumping
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DOI：
10.1038/s41586-021-03688-9
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发表时间：
2021-08-05
期刊：
影响因子：
64.8
通讯作者：
Rechtsman, Mikael C.
中科院分区：
文献类型：
--
作者：
Jurgensen, Marius;Mukherjee, Sebabrata;Rechtsman, Mikael C.
波输运的拓扑保护最初是在二维电子气中的量子霍尔效应的背景下观察到的（1），已被证明广泛应用于一系列物理平台，包括光子学（2-5），光学晶格中的超冷原子（6-8）和其他（9-12）。也就是说，这种系统的行为可能与电子情况非常不同，特别是当粒子间相互作用或非线性起主要作用时（13-22）。无源泵浦（23）是一个一维模型，它使用降维的概念来捕获量子霍尔效应中传输的拓扑量子化：一个随时间变化的势函数在数学上映射到概念上的第二维中的动量坐标上（24-34）。重要的是，量子化假设在费米能量以下的电子带均匀填充，或者非平衡玻色子系统的等效占据。在这里，我们从理论上提出和实验证明量子化的非线性无源泵浦光子的频带，这是决定性的不均匀占用。在我们的系统中，非线性通过孤子的形成和自发的破缺分岔对非线性输运起作用。量子化是因为在每个泵浦周期之后，以给定晶胞为中心的瞬时孤子解是相同的，直到平移不变性;这是一种与传统无源泵浦完全不同的机制。结果表明，非线性和粒子间相互作用可以诱导量子化的输运和拓扑行为，而没有线性对应物。非线性被证明是通过孤子运动诱导量子化的拓扑输运。具体地说，我们证明了非线性无源泵浦光子在波导阵列与非均匀占据的能带。
The topological protection of wave transport, originally observed in the context of the quantum Hall effect in two-dimensional electron gases(1), has been shown to apply broadly to a range of physical platforms, including photonics(2-5), ultracold atoms in optical lattices(6-8) and others(9-12). That said, the behaviour of such systems can be very different from the electronic case, particularly when interparticle interactions or nonlinearity play a major role(13-22). A Thouless pump(23) is a one-dimensional model that captures the topological quantization of transport in the quantum Hall effect using the notion of dimensional reduction: an adiabatically, time-varying potential mathematically maps onto a momentum coordinate in a conceptual second dimension(24-34). Importantly, quantization assumes uniformly filled electron bands below a Fermi energy, or an equivalent occupation for non-equilibrium bosonic systems. Here we theoretically propose and experimentally demonstrate quantized nonlinear Thouless pumping of photons with a band that is decidedly not uniformly occupied. In our system, nonlinearity acts to quantize transport via soliton formation and spontaneous symmetry-breaking bifurcations. Quantization follows from the fact that the instantaneous soliton solutions centred upon a given unit cell are identical after each pump cycle, up to translation invariance; this is an entirely different mechanism from traditional Thouless pumping. This result shows that nonlinearity and interparticle interactions can induce quantized transport and topological behaviour without a linear counterpart.Nonlinearity is shown to induce quantized topological transport via soliton motion; specifically, we demonstrate nonlinear Thouless pumping of photons in waveguide arrays with a non-uniformly occupied energy band.