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，特别是在平衡动力学的背景下，仍然在很大程度上无法与传统的数值方法。在这个项目中，我们将使用一种新的混合镊子晶格，在状态依赖的光学晶格中使用Yb原子，对简化的晶格规范理论（LGT）进行量子模拟，这将提供量子气体显微镜提供的高分辨率成像和操纵技术。主要目标是研究与物质耦合的U（1）LGT中的非遍历性和非平衡现象。该实现利用LGT的量子链路模型（QLM），其中规范场的希尔伯特空间被截断和有限的制定。最简单的实现可以映射到自旋1/2算子，在我们的情况下，由Yb的两个光学时钟状态表示。这两种状态也便于实现与远失谐激光束的状态相关的潜力。借助紧聚焦光镊束提供的依赖于局部状态的寻址，我们将实现一个晶格势，其中动力学受到强烈约束，以满足高斯定律的QLM。隧穿项主要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穿或拉曼耦合，这应该能够实现长的相干时间，如非遍历现象的研究所需的。本地寻址和观测技术与高精度光谱学相结合的光学时钟过渡促进实现满足高斯定律的初始状态。这打开了大门，在我们的模型中预测的约束-解除约束过渡的实验研究，并探讨无序的本地化在一维，这可能会发生由于高斯定律施加的局部约束。此外，实验实施的目的是为了研究两个维度的失衡现象，我们将在第一个资助期结束时开始与该拟议研究单位的理论小组密切合作进行调查。

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.