Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ${}^{88}{\mathrm{Sr}}^{+}$ Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results—for example—in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.

中文翻译：

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被困的里德堡离子链中的远程多体相互作用和三体抗封锁

被困的里德伯格离子代表了一个灵活的平台，用于量子模拟和信息处理，结合了对电子和振动自由度的高度控制。将离子单独激发到较高的里德堡能级的可能性提供了一个系统，在该系统中，可以通过外部激光场设计和调整激发离子对之间的强相互作用。我们表明，里德伯格对相互作用和集体运动模式之间的耦合产生了有效的远程和多体相互作用，其中包括两个，三个和四个体项。它们的形状，强度和范围可以通过离子阱参数进行控制，并且在很大程度上取决于离子晶体的平衡构型和振动模式。通过关注实验上可行的准一维设置${}^{88}{r}^{+}$Rydberg离子，我们证明多体相互作用通过与（例如）结构相变相关的软模式的出现而得到增强。这对多体电子状态产生了显着影响，例如，导致了三体抗阻滞作用，该作用可用作检测Rydberg离子链中结构相变的灵敏探针。我们的研究揭示了被捕获的里德堡离子提供的可能性，以研究由增强的多体相互作用驱动的奇异物质相和量子动力学。