二维离子晶体中的旋-旋相互作用和量子磁性
Hexagonal Plaquette Spin-spin Interactions and Quantum Magnetism in a Two-dimensional Ion Crystal
摘要：
我们提出了一个捕获离子的计划途中实现自旋哈密顿的Kagome晶格，在低能量下，所描述的紧急Z2规范场，并支持拓扑量子自旋液体基态。在我们的方案中的使能元素是在一个二维离子晶体中的六角元格自旋-自旋相互作用。为此，晶体的声子模式光谱通过驻波光学势或通过使用里德伯激发离子来设计，从而在从整个二维晶体中选择的六边形离子周围产生局部声子模式。当受到状态依赖的光偶极力作用时，这些定制的模式可以介导六边形元格上的离子量子比特之间的自旋-自旋相互作用。我们讨论了如何利用这些相互作用来模拟一个广义Balents-Fisher-Girvin模型在最小的情况下，一个和两个斑块。该模型是一个典型的哈密顿量，其中规范场是经典基态流形上的涌现自由度。在实际情况下，我们显示了出现的离散高斯定律以及动力学的规范不变的背景下，使用两个plaquettes捕获的离子自旋系统的解除限制的电荷激发。所提出的方案在原则上允许进一步缩放在未来的囚禁离子量子模拟器，我们的结论是，我们的工作将铺平道路，对紧急规范理论和量子自旋液体在囚禁离子系统的模拟。
英文摘要：
We propose a trapped ion scheme en route to realize spin Hamiltonians on a Kagome lattice which, at low energies, are described by emergent Z2 gauge fields, and support a topological quantum spin liquid ground state. The enabling element in our scheme is the hexagonal plaquette spin-spin interactions in a 2D ion crystal. For this, the phonon-mode spectrum of the crystal is engineered by standing-wave optical potentials or by using Rydberg excited ions, thus generating localized phonon-modes around a hexagon of ions selected out of the entire two-dimensional crystal. These tailored modes can mediate spin-spin interactions between ion-qubits on a hexagonal plaquette when subject to state-dependent optical dipole forces. We discuss how these interactions can be employed to emulate a generalized Balents-Fisher-Girvin model in minimal instances of one and two plaquettes. This model is an archetypical Hamiltonian in which gauge fields are the emergent degrees of freedom on top of the classical ground state manifold. Under realistic situations, we show the emergence of a discrete Gauss's law as well as the dynamics of a deconfined charge excitation on a gauge-invariant background using the two-plaquettes trapped ions spin-system. The proposed scheme in principle allows further scaling in a future trapped ion quantum simulator, and we conclude that our work will pave the way towards the simulation of emergent gauge theories and quantum spin liquids in trapped ion systems.
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