Photon-mediated interaction between quantum emitters in engineered photonic baths is an emerging area of quantum optics. At the same time, non-Hermitian (NH) physics is currently thriving, spurred by the exciting possibility to access new physics in systems ruled by non-trivial NH Hamiltonians—in particular, photonic lattices—which can challenge longstanding tenets such as the Bloch theory of bands. Here, we combine these two fields and study the exotic interaction between emitters mediated by the photonic modes of a lossy photonic lattice described by a NH Hamiltonian. We show in a paradigmatic case study that structured losses in the field can seed exotic emission properties. Photons can mediate dissipative, fully non-reciprocal interactions between emitters with range critically dependent on the loss rate. When this loss rate corresponds to a bare-lattice exceptional point, the effective couplings are exactly nearest neighbor, implementing a dissipative, fully non-reciprocal Hatano–Nelson model. Counterintuitively, this can occur irrespective of the lattice boundary conditions. Thus photons can mediate an effective emitter’s Hamiltonian which is translationally invariant despite the fact that the field is not. We interpret these effects in terms of metastable atom–photon dressed states, which can be exactly localized on only two lattice cells or extended across the entire lattice. These findings introduce a paradigm of light-mediated interactions with unprecedented features such as non-reciprocity, non-trivial dependence on field boundary conditions, and range tunability via a loss rate.

中文翻译：

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由非厄米特光子浴介导的奇异相互作用

工程光子浴中量子发射器之间的光子介导相互作用是量子光学的一个新兴领域。与此同时，非厄米特 (NH) 物理学目前正在蓬勃发展，这得益于在非平凡的 NH 哈密顿量（特别是光子晶格）统治的系统中获得新物理学的令人兴奋的可能性，这可能挑战诸如布洛赫等长期存在的原则能带理论。在这里，我们将这两个领域结合起来，研究由 NH 哈密顿量描述的有损光子晶格的光子模式介导的发射器之间的奇异相互作用。我们在一个典型的案例研究中展示了结构化损失在该领域可以播种奇异的发射特性。光子可以调节发射器之间的耗散性、完全非互易的相互作用，其范围严重依赖于损耗率。当此损失率对应于裸晶格异常点时，有效耦合恰好是最近邻，实现了耗散的、完全非互易的 Hatano-Nelson 模型。与直觉相反，无论晶格边界条件如何，这都可能发生。因此，光子可以调节有效发射器的哈密顿量，尽管场不是这样，但它是平移不变的。我们用亚稳态原子 - 光子修饰状态来解释这些效应，它可以精确地定位在两个晶格上或延伸到整个晶格上。