论文标题
通过拓扑扩增恢复非铁人散装对应
Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
论文作者
论文摘要
非热（NH）晶格汉密尔顿人表现出一种独特的能量差距和对边界条件的极端敏感性。由于NH皮肤效应，边缘和散装状态之间的分离被模糊，并且（常规）散装对应关系丢失。在这里，我们恢复了最典型的NH汉密尔顿人阶级的庞大信函，即具有一个复杂乐队且没有对称性的人。我们从驱动的腔阵列的（平均场）无条件演化中获得所需的NH Hamiltonian，其中NH术语（以非重新性跳跃振幅，增益和损失的形式）通过耦合到（工程和非工程储层）。这种方法消除了拓扑不变的定义中的任意性，因为与复杂能量转移不同的指示光谱不被视为等效。复杂平面的起源为评估拓扑不变的常见参考（基数）提供了。这意味着在拓扑上是非平凡的哈密顿人只是那些具有点间隙的严格子集，而NH皮肤效应没有拓扑起源。 We analyze the NH Hamiltonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value $ν$ of the topological invariant defined in the bulk corresponds to $\vert ν\vert$ singular vectors exponentially localized at the system edge under open boundary conditions, in which the sign of $ν$ determines which edge.非平凡拓扑表现为具有系统尺寸增益指数的相干输入的定向扩增。我们的工作解决了NH拓扑阶段理论的一个杰出问题，并开辟了拓扑光子学方面的新途径。
Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and extreme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional) bulk-boundary correspondence is lost. Here, we restore the bulk-boundary correspondence for the most paradigmatic class of NH Hamiltonians, namely those with one complex band and without symmetries. We obtain the desired NH Hamiltonian from the (mean-field) unconditional evolution of driven-dissipative cavity arrays, in which NH terms -- in the form of non-reciprocal hopping amplitudes, gain and loss -- are explicitly modeled via coupling to (engineered and non-engineered) reservoirs. This approach removes the arbitrariness in the definition of the topological invariant, as point-gapped spectra differing by a complex-energy shift are not treated as equivalent; the origin of the complex plane provides a common reference (base point) for the evaluation of the topological invariant. This implies that topologically non-trivial Hamiltonians are only a strict subset of those with a point gap and that the NH skin effect does not have a topological origin. We analyze the NH Hamiltonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value $ν$ of the topological invariant defined in the bulk corresponds to $\vert ν\vert$ singular vectors exponentially localized at the system edge under open boundary conditions, in which the sign of $ν$ determines which edge. Non-trivial topology manifests as directional amplification of a coherent input with gain exponential in system size. Our work solves an outstanding problem in the theory of NH topological phases and opens up new avenues in topological photonics.
