论文标题
在拉曼耦合的玻色 - 因施泰因冷凝物中编码一维拓扑量规理论
Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate
论文作者
论文摘要
拓扑规程的理论提供了某些强相关系统的有效描述，一个典型的例子是Chern-Simons量表的分数量子厅态。受控量子系统中的工程拓扑规程理论既概念化又实用，因为它将提供对具有异国情调激发的系统的访问，例如Anyons，而无需强大的相关性。在这里，我们讨论了一种旨在设计手性BF理论的方案，这是一种拓扑规理论的最小模型，该模型与Chern-Simons理论的一维还原相对应。使用该理论的局部保护定律，我们将其量子Hamitonian编码为具有手性相互作用的超低量子气体。建立在Edmonds等人的开创性建议的基础上。 （Phys。Rev.Lett。110，085301（2013）），我们展示了如何在带有不平衡散射长度的拉曼耦合的Bose-Einstein冷凝物中实施，正如我们最近在实验中实现的那样（Frölian等人，自然608，293（202222））。我们从仪表理论的角度讨论了手性冷凝物的特性，并通过数值模拟评估有效量子描述的有效量子描述的有效性。我们的方法奠定了实现拓扑仪理论的基础。
Topological gauge theories provide powerful effective descriptions of certain strongly correlated systems, a prime example being the Chern-Simons gauge theory of fractional quantum Hall states. Engineering topological gauge theories in controlled quantum systems is of both conceptual and practical importance, as it would provide access to systems with exotic excitations such as anyons without the need for strong correlations. Here, we discuss a scheme to engineer the chiral BF theory, a minimal model of a topological gauge theory corresponding to a one-dimensional reduction of the Chern-Simons theory, with ultracold atoms. Using the local conservation laws of the theory, we encode its quantum Hamitonian into an ultracold quantum gas with chiral interactions. Building on a seminal proposal by Edmonds et al. (Phys. Rev. Lett. 110, 085301 (2013)), we show how to implement it in a Raman-coupled Bose-Einstein condensate with imbalanced scattering lengths, as we have recently realized experimentally (Frölian et al., Nature 608, 293 (2022)). We discuss the properties of the chiral condensate from a gauge theory perspective, and assess the validity of the effective quantum description for accessible experimental parameters via numerical simulations. Our approach lays the foundation for realizing topological gauge theories in higher dimensions with Bose-Einstein condensates.
