Topological photonics is an emerging research area that focuses on the topological states of classical light. Here we reveal the topological phases that are intrinsic to the quantum nature of light, i.e. solely related to the quantized Fock states and the inhomogeneous coupling strengths between them. The Hamiltonian of two cavities coupled with a two-level atom is an intrinsic one-dimensional Su-Schriefer-Heeger model of Fock states. By adding another cavity, the Fock-state lattice is extended to two dimensions with a honeycomb structure, where the strain due to the inhomogeneous coupling strengths of the annihilation operator induces a Lifshitz topological phase transition between a semimetal and three band insulators within the lattice. In the semimetallic phase, the strain is equivalent to a pseudomagnetic field, which results in the quantization of the Landau levels and the valley Hall effect. We further construct an inhomogeneous Fock-state Haldane model where the topological phases can be characterized by the topological markers. With d cavities being coupled to the atom, the lattice is extended to d − 1 dimensions without an upper limit. In this study we demonstrate a fundamental distinction between the topological phases in quantum and classical optics and provide a novel platform for studying topological physics in dimensions higher than three.

中文翻译：

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量化光的拓扑相位

拓扑光子学是一个新兴的研究领域，专注于经典光的拓扑状态。在这里，我们揭示了光的量子性质所固有的拓扑相，即仅与量化的 Fock 状态和它们之间的非均匀耦合强度有关。与两能级原子耦合的两个腔的哈密顿量是 Fock 状态的固有一维 Su-Schriefer-Heeger 模型。通过添加另一个腔，Fock 状态晶格扩展到具有蜂窝结构的二维，其中由于湮灭算子的不均匀耦合强度引起的应变引起晶格内半金属和三个带绝缘体之间的 Lifshitz 拓扑相变。在半金属相中，应变相当于伪磁场，这导致了朗道能级和谷霍尔效应的量化。我们进一步构建了一个非均匀 Fock-state Haldane 模型，其中拓扑相可以通过拓扑标记来表征。和d 个空腔与原子耦合，晶格扩展到d - 1 维，没有上限。在这项研究中，我们展示了量子光学和经典光学中拓扑相之间的根本区别，并为研究高于三维的拓扑物理学提供了一个新平台。