Measuring the knot of non-Hermitian degeneracies and non-commuting braids
Measuring the knot of non-Hermitian degeneracies and non-commuting braids
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DOI：
10.1038/s41586-022-04796-w
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发表时间：
2022-07-14
期刊：
影响因子：
64.8
通讯作者：
Harris, Jack G. E.
中科院分区：
文献类型：
--
作者：
Patil, Yogesh S. S.;Holler, Judith;Harris, Jack G. E.
任何耦合振荡器系统都可以通过其共振频率(或本征频率)的频谱来表征，该频谱可以通过改变系统的参数来调节。控制参数和特征频谱之间的关系是一系列应用的核心(1-3)。然而，这种关系的基本方面仍然知之甚少。例如，如果控制沿着返回到其起点的路径变化(即，围绕一个“循环”)，则系统的频谱必须返回到其自身。在厄米特系统中(即无损和互易)，这个过程是微不足道的，每个共振频率都会恢复到它的原始值。然而，在本征频率复杂的非厄米系统中，频谱可能会以一种拓扑上非平凡的方式返回到自己，这一现象被称为谱流。频谱流由控制环路环绕简并的方式来确定，并且当N=2(其中N是系统中的振荡器的数目)(4，5)时，该关系被很好地理解。在这里，我们将这种描述扩展到任意N。我们证明了控制回路通常产生特征频率的辫子，并且对于N>；2，这些辫子形成了反映退化空间的非平凡几何的非阿贝尔群。我们利用腔光机械系统对N=3时的这些特性进行了实验验证。
Any system of coupled oscillators may be characterized by its spectrum of resonance frequencies (or eigenfrequencies), which can be tuned by varying the system's parameters. The relationship between control parameters and the eigenfrequency spectrum is central to a range of applications(1-3). However, fundamental aspects of this relationship remain poorly understood. For example, if the controls are varied along a path that returns to its starting point (that is, around a 'loop'), the system's spectrum must return to itself. In systems that are Hermitian (that is, lossless and reciprocal), this process is trivial and each resonance frequency returns to its original value. However, in non-Hermitian systems, where the eigenfrequencies are complex, the spectrum may return to itself in a topologically non-trivial manner, a phenomenon known as spectral flow. The spectral flow is determined by how the control loop encircles degeneracies, and this relationship is well understood for N = 2 (where N is the number of oscillators in the system)(4,5). Here we extend this description to arbitrary N. We show that control loops generically produce braids of eigenfrequencies, and for N > 2 these braids form a non-Abelian group that reflects the non-trivial geometry of the space of degeneracies. We demonstrate these features experimentally for N = 3 using a cavity optomechanical system.