Prediction of Toric Code Topological Order from Rydberg Blockade
Prediction of Toric Code Topological Order from Rydberg Blockade
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DOI：
10.1103/physrevx.11.031005
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发表时间：
2020-11
影响因子：
12.5
通讯作者：
R. Verresen;M. Lukin;A. Vishwanath
中科院分区：
文献类型：
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作者：
R. Verresen;M. Lukin;A. Vishwanath
在范式环码中遇到的$\mathbb Z_2$拓扑顺序的物理实现已被证明是一个难以捉摸的目标。我们表明，物质的这一阶段可以在二维强相互作用的里德伯原子阵列中产生。我们的建议是利用定位在红宝石晶格上的原子，通过里德堡封锁机制耦合。首先，我们证明了阻滞模型在kagome晶格上有效地实现了具有单位动力学项的单体-二聚体模型，并利用数值密度矩阵重整化群方法获得了其相图。我们发现了一个拓扑量子液体（TQL），这可以通过多种测量来证明，包括(i)两个无特征相之间的连续过渡，（ii）在各种几何形状中测量的拓扑纠缠熵$\ln 2$, （iii）退化的拓扑基态和（iv）基态重叠的期望模矩阵。接下来，我们将证明TQL可以持续包含现实的、代数衰减的范德华相互作用$V(r) \sim 1/r^6$。此外，我们可以直接访问该模型的拓扑环算子，可以使用动态协议进行实验测量，提供TQL阶段的“确凿证据”实验签名。最后，我们展示了如何捕获突现的任意子和实现不同的拓扑边界条件，并讨论了探索容错量子存储器的意义。
The physical realization of $\mathbb Z_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We show that this phase of matter can be created in a two-dimensional array of strongly interacting Rydberg atoms. Our proposal makes use of atoms localized on the sites of a ruby lattice, coupled via a Rydberg blockade mechanism. First, we show that the blockade model effectively realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term, and we obtain its phase diagram using the numerical density matrix renormalization group method. We find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of $\ln 2$ as measured in various geometries, (iii) degenerate topological ground states and (iv) the expected modular matrix from ground state overlap. Next, we show that the TQL can persist upon including realistic, algebraically-decaying van der Waals interactions $V(r) \sim 1/r^6$. Moreover, we can directly access the topological loop operators of this model, which can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase. Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.