The interaction between quantized electromagnetic fields in cavities and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interactions and quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling of cavity-QED have been explored in several settings, wherein the light-matter coupling rate becomes comparable to (ultrastrong coupling) or even exceeds (deep-strong coupling) the photon frequency. These ultrastrong coupling regimes can give rise to new physical effects and applications, and they challenge our understanding of cavity QED; fundamental issues like the proper definition of subsystems, their quantum measurements, the structure of light-matter ground states, and the analysis of time-dependent interactions are subject to gauge ambiguities that lead to even qualitatively distinct predictions. The resolution of these ambiguities is important for understanding and designing next-generation quantum devices that can operate in extreme coupling regimes. Here we discuss and provide solutions to these ambiguities by adopting an approach based on operational procedures involving measurements on the individual light and matter components of the interacting system.

中文翻译：

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腔体QED中的量规自由度，量子测量和时间相关的相互作用

空腔中的量化电磁场与天然或人造原子之间的相互作用在增进我们对光物质相互作用和量子技术的理解中起着至关重要的作用。最近，已经在几种设置中探索了除腔QED的弱和强光-质耦合之外的新机制，其中光-质耦合速率变得与（超强耦合）相当，甚至超过（深-强耦合）光子频率。 。这些超强耦合机制会带来新的物理效应和应用，并且挑战了我们对腔体QED的理解。基本问题，例如子系统的正确定义，它们的量子测量，光物质基态的结构，以及与时间相关的相互作用的分析受制于模棱两可，甚至导致定性上截然不同的预测。这些歧义的解决对于理解和设计可以在极端耦合条件下运行的下一代量子器件很重要。在这里，我们通过采用一种基于操作程序的方法来讨论这些歧义并提供解决方案，这些方法包括对交互系统的各个光和物质成分进行测量。