We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose–Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.

我们回顾了量子气腔 QED 领域的最新发展和现状。自从第一次在一个由玻色-爱因斯坦凝聚体耦合到高Q量子化电磁模式组成的系统中原子自排序的实验证明以来光学腔，该领域在过去十年中迅速发展。复合量子气腔系统提供了实现、模拟和实验测试基本固态哈密顿量的机会，以及实现超越传统凝聚态场景的非平衡多体现象。这取决于使用定制的泵浦激光器和动态腔场在开放量子环境中设计和控制原子的光子诱导可调范围相互作用势的独特可能性。值得注意的例子包括具有长程相互作用的类似哈伯德模型，表现出晶格-超固相、超磁序和准晶对称性，以及动态规范电位和非平衡拓扑相的出现。实验已经成功地将自旋极化和自旋量子气体加载到各种腔体几何结构中，并设计出多功能可调范围的原子相互作用。这导致了对自发离散和连续对称性破坏的实验观察，软模式以及超固体、密度和自旋自排序、动态自旋轨道耦合和非平衡动态自排序相等的出现。此外，量子气体腔设置为量子增强测量提供了新平台。在这篇评论中，我们从基本模型的介绍开始，这导致了对自发离散和连续对称性破坏的实验观察，软模式以及超固体、密度和自旋自排序、动态自旋轨道耦合和非平衡动态自排序相等的出现。此外，量子气体腔设置为量子增强测量提供了新平台。在这篇评论中，我们从基本模型的介绍开始，这导致了对自发离散和连续对称性破坏的实验观察，软模式以及超固体、密度和自旋自排序、动态自旋轨道耦合和非平衡动态自排序相等的出现。此外，量子气体腔设置为量子增强测量提供了新平台。在这篇评论中，我们从基本模型的介绍开始，在教学上总结了广泛的理论发展，并将它们与当前和不久的将来最先进的实验相结合。