Stable composite objects, such as hadrons, nuclei, atoms, molecules and superconducting pairs, formed by attractive forces are ubiquitous in nature. By contrast, composite objects stabilized by means of repulsive forces were long thought to be theoretical constructions owing to their fragility in naturally occurring systems. Surprisingly, the formation of bound atom pairs by strong repulsive interactions has been demonstrated experimentally in optical lattices¹. Despite this success, repulsively bound particle pairs were believed to have no analogue in condensed matter owing to strong decay channels. Here we present spectroscopic signatures of repulsively bound three-magnon states and bound magnon pairs in the Ising-like chain antiferromagnet BaCo₂V₂O₈. In large transverse fields, below the quantum critical point, we identify repulsively bound magnon states by comparing terahertz spectroscopy measurements to theoretical results for the Heisenberg–Ising chain antiferromagnet, a paradigmatic quantum many-body model^2,3,4,5. Our experimental results show that these high-energy, repulsively bound magnon states are well separated from continua, exhibit notable dynamical responses and, despite dissipation, are sufficiently long-lived to be identified. As the transport properties in spin chains can be altered by magnon bound states, we envision that such states could serve as resources for magnonics-based quantum information processing technologies^6,7,8.

由吸引力形成的稳定复合物体，如强子、原子核、原子、分子和超导对，在自然界中无处不在。相比之下，通过排斥力稳定的复合物体长期以来被认为是理论构造，因为它们在自然存在的系统中很脆弱。令人惊讶的是，通过强排斥相互作用形成束缚原子对已经在光学晶格 ¹ 中得到了实验证明。尽管取得了这一成功，但由于强衰变通道，排斥束缚粒子对被认为在凝聚态物质中没有类似物。在这里，我们提出了类伊辛链反铁磁体 BaCo ₂ V ₂ O ₈ 中排斥束缚三磁振子态和束缚磁振子对的光谱特征。在大横向场中，低于量子临界点，我们通过将太赫兹光谱测量结果与海森堡-伊辛链反铁磁体（一种典型的量子多体模型 ^2,3,4,5 ）的理论结果进行比较来识别排斥束缚磁振子态。我们的实验结果表明，这些高能、排斥束缚的磁振子态与连续体很好地分离，表现出显着的动力学响应，尽管存在耗散，但其寿命足够长，足以被识别。由于自旋链中的传输特性可以通过磁振子束缚态改变，我们设想这些态可以作为基于磁振子的量子信息处理技术的资源 ^6,7,8 。