In the regime of deep strong light–matter coupling, the coupling strength exceeds the transition energies of the material1–3, fundamentally changing its properties4,5; for example, the ground state of the system contains virtual photons and the internal electromagnetic field gets redistributed by photon self-interaction1,6. So far, no electronic excitation of a material has shown such strong coupling to free-space photons. Here we show that three-dimensional crystals of plasmonic nanoparticles can realize deep strong coupling under ambient conditions, if the particles are ten times larger than the interparticle gaps. The experimental Rabi frequencies (1.9 to 3.3 electronvolts) of face-centred cubic crystals of gold nanoparticles with diameters between 25 and 60 nanometres exceed their plasmon energy by up to 180 per cent. We show that the continuum of photons and plasmons hybridizes into polaritons that violate the rotating-wave approximation. The coupling leads to a breakdown of the Purcell effect—the increase of radiative damping through light–matter coupling—and increases the radiative polariton lifetime. The results indicate that metallic and semiconducting nanoparticles can be used as building blocks for an entire class of materials with extreme light–matter interaction, which will find application in nonlinear optics, the search for cooperative effects and ground states, polariton chemistry and quantum technology4,5. Photons and plasmons hybridize into polaritons in three-dimensional crystals of plasmonic nanoparticles, leading to deep strong light–matter coupling and the breakdown of the Purcell effect.

中文翻译：

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等离子体纳米粒子晶体中的深强光-物质耦合

在深度强光-物质耦合状态下，耦合强度超过材料1-3的跃迁能，从根本上改变其性质4,5；例如，系统的基态包含虚拟光子，内部电磁场通过光子自相互作用重新分布1,6。到目前为止，还没有一种材料的电子激发表现出与自由空间光子如此强的耦合。在这里，我们表明，如果粒子比粒子间间隙大十倍，等离子体纳米粒子的三维晶体可以在环境条件下实现深度强耦合。直径在 25 到 60 纳米之间的金纳米粒子的面心立方晶体的实验拉比频率（1.9 到 3.3 电子伏特）超过了它们的等离子体能量高达 180%。我们表明光子和等离子体的连续体杂交成违反旋转波近似的极化子。这种耦合会导致珀塞尔效应的破坏——通过光-物质耦合增加辐射阻尼——并增加辐射极化子的寿命。结果表明，金属和半导体纳米粒子可以用作具有极端光-物质相互作用的整类材料的构建块，这将在非线性光学、协同效应和基态的搜索、极化子化学和量子技术中找到应用。 5. 光子和等离子体在等离子体纳米粒子的三维晶体中杂交成极化子，导致深度强光-物质耦合和珀塞尔效应的破坏。