Exploring non-ergodicity in lattice gauge theories with fermionic Yb

规范理论对于我们理解自然是必不可少的，它们的性质为跨学科研究提供了令人兴奋的新机会。不幸的是，许多基本性质，特别是在非平衡动力学的背景下，仍然在很大程度上无法用传统的数值方法来获得。在这个项目中，我们将使用一种新的混合镊子-晶格来对简化的晶格规范理论(LGT)进行量子模拟，该晶格使用依赖于状态的光学晶格中的Yb原子，这将提供由量子气体显微镜提供的高分辨率成像和操纵技术。主要目的是研究与物质耦合的U(1)LGT中的非遍历和非平衡现象。该实现利用了量子链接模型(QLMS)中的LGT公式，其中规范场的希尔伯特空间是截断的和有限的。最简单的实现可以映射到自旋1/2算符，在我们的例子中，它由Yb的两个光时钟态表示。这两个态也便于用远失谐的激光束实现与状态相关的势。在紧聚焦光钳光束提供的局域态相关寻址的帮助下，我们将实现晶格势，在晶格势中，动力学受到强烈的约束，以满足QLM的高斯定律。主要的隧道项是两个原子的关联跳跃过程，可以映射到U(1)QLm上。该方案不需要任何激光辅助隧道或拉曼耦合，这将使研究非遍历现象所需的长相干时间成为可能。光学时钟跃迁的局域寻址和观测技术与高精度光谱相结合，有助于实现满足高斯定律的初始态。这为我们的模型中预测的禁闭-解禁闭转变的实验研究打开了大门，并探索一维无序局域化，这可能是由于高斯定律施加的局域约束而发生的。此外，实施实验的目的是研究两个方面的失衡现象，我们将在第一个资助期结束时与拟议的研究股的理论小组密切合作，开始调查这一现象。

Gauge theories are essential for our understanding of nature and their properties provide exciting new opportunities for interdisciplinary research. Unfortunately, many fundamental properties, especially in the context of out-of-equilibrium dynamics, remain largely inaccessible with conventional numerical methods. Within this project we are going to perform quantum simulation of simplified lattice gauge theories (LGTs) using a new hybrid tweezer-lattice using Yb atoms in state-dependent optical lattices, which will offer high-resolution imaging and manipulation techniques provided by quantum gas microscopy. The main goal is to study non-ergodicity and out-of-equilibrium phenomena in U(1) LGTs coupled to matter. The implementation makes use of the formulation of LGTs in terms of quantum link models (QLMs), where the Hilbert space of the gauge field is truncated and finite. The simplest realization can be mapped to spin-1/2 operators, which in our case are represented by the two optical clock states of Yb. These two states also facilitate a convenient implementation of state-dependent potentials with far-detuned laser beams. With the help of local state-dependent addressing provided by tightly-focused optical tweezer beams, we are going to realize a lattice potential, where the dynamics is strongly constrained in order to fulfill Gauss’s law for the QLM. The dominant tunneling term is a correlated hopping process of two atoms, which can be mapped onto a U(1) QLM. The scheme does not require any laser-assisted tunneling or Raman coupling, which should enable long coherence times, as needed for the study of non-ergodic phenomena. The local addressing and observation techniques combined with high-precision spectroscopy on the optical clock transition facilitates the implementation of initial states that fulfill Gauss’s law. This opens the door to experimental studies of the predicted confinement-deconfinement transition in our model and to explore disorder-free localization in one-dimension, which may occur due to the local constraints imposed by Gauss’s law. Moreover, the experimental implementation is designed in order to study out-of-equilibrium phenomena in two dimensions, which we will start to investigate in strong collaboration with the theory groups of this proposed Research Unit towards the end of the first funding period.