The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Because of the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al., Nature (London) 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors; i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one, or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in nonchiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.

中文翻译：

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动态环绕特殊点：环绕环的原位控制和起点的作用

非Hermitian系统最令人着迷的特性是在汉密尔顿矩阵变得有缺陷的例外点（EPs）附近发现的。由于能量的黎曼面接近EP的复杂拓扑结构以及绝热定理的非厄密性破坏，非厄密系统的状态演化要比厄密系统的复杂得多。例如，最近的实验工作[Doppler等。，大自然（伦敦） 537，76（2016）]证明了动态包围EP可以导致手性行为。即，沿不同方向环绕EP会导致不同的输出状态。在这里，我们提出了一个带有两个EP的耦合铁磁波导系统，并设计了一个实验装置，其中状态演化的轨迹可以就地控制。使用可调外部场，使我们能够实验性地动态包围零个，一个甚至两个EP。可调性使我们能够控制参数空间中的环绕轨迹，包括环绕环的大小和起点/终点。我们发现动力学是否是手性的实际上取决于循环的起点。特别地，在奇偶校验时间破碎阶段中以起始点动态环绕EP会导致非手性行为，从而无论环绕沿哪个方向，输出状态都是相同的。所提出的系统是一个有用的平台，可用于探索非Hermitian系统中的能量表面拓扑和状态演化的动力学，并且很可能会发现在受外部参数控制的模式切换中的应用。