Systems consisting of cold atoms trapped near photonic crystal waveguides have recently emerged as an exciting platform for quantum atom-light interfaces. Such a system enables realization of tunable long-range interactions between internal states of atoms (spins), mediated by guided photons. Currently, experimental platforms are still limited by low filling fractions, where the atom number is much smaller than the number of sites at which atoms can potentially be trapped. Here, we show that this regime in fact enables interesting many-body quantum phenomena, which are typically associated with short-range disordered systems. As an example, we show how the system can realize the so-called “random singlet phase” (RSP), in which all atoms pair into entangled singlets, but the pairing occurs over a distribution of ranges as opposed to nearest neighbors. We use a renormalization group method to obtain the distribution of spin entanglement in the RSP, and show how this state can be approximately reached via adiabatic evolution from the ground state of a noninteracting Hamiltonian. We also discuss how experimentally this RSP can be observed. We anticipate that this work will accelerate the route toward the exploration of strongly correlated matter in atom-nanophotonics interfaces, by avoiding the requirement of perfectly filled lattices.

中文翻译：

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冷原子的随机单线态耦合到光子晶体波导

由被困在光子晶体波导附近的冷原子组成的系统最近已成为量子原子-光界面的一个令人兴奋的平台。这样的系统能够实现由引导光子介导的原子内部状态（自旋）之间的可调长程相互作用。目前，实验平台仍然受到低填充率的限制，其中原子数远小于原子可能被捕获的位点数。在这里，我们展示了这种机制实际上实现了有趣的多体量子现象，这些现象通常与短程无序系统相关。作为一个例子，我们展示了系统如何实现所谓的“随机单线态”（RSP），其中所有原子都配对成纠缠的单线态，但配对发生在范围分布上，而不是最近邻。我们使用重整化群方法来获得 RSP 中自旋纠缠的分布，并展示如何从非相互作用的哈密顿量的基态通过绝热演化近似达到这种状态。我们还讨论了如何通过实验观察到这个 RSP。我们预计这项工作将通过避免完全填充晶格的要求，加速探索原子-纳米光子学界面中强相关物质的途径。我们还讨论了如何通过实验观察到这个 RSP。我们预计这项工作将通过避免完全填充晶格的要求，加速探索原子-纳米光子学界面中强相关物质的途径。我们还讨论了如何通过实验观察到这个 RSP。我们预计这项工作将通过避免完全填充晶格的要求，加速探索原子-纳米光子学界面中强相关物质的途径。