Next Generation Quantum Simulators: From DYNAMIcal Gauge Fields to Lattice Gauge ThEory

截至今天，量子模拟器（QS）是可以解决，加深我们的理解，并最终解决当代科学的一些最具挑战性的问题的系统：从量子多体动力学，通过静态和瞬态高Tc超导，新材料的设计。在DYNAMITE中，我们将设计，在实验室中实现，并描述新一代具有超冷原子的QS。随着实验复杂度的增加，这涉及到：（WP1）具有统计规范场的系统，即具有密度依赖规范场的“单组分”晶格或连续统系统改变粒子的有效量子统计量并实现拓扑规范理论；（WP2）动力晶格中的系统，“物质”存在于位点上，附加的动力场/粒子存在于键上；（WP3）晶格规范理论模型（LGT），从Abelian （Z2， U(1)）系统到非Abelian局部规范对称。这样的系统解决了来自凝聚态物理、核物理、高能物理和材料科学的问题：特别是，WP1允许人们在连续介质中设计拓扑规范理论，并设计和控制新型的拓扑和手性秩序，可能应用于量子计算和量子存储器。这里的理论和实验目标是为规范场量身定制适当的物质依赖，这对应于正确施加规范理论的局部对称约束。WP2允许人们设计和研究拓扑秩序和对称破缺之间的相互作用。没有规范不变性的简单系统已经在实验室中得到了模拟，这使我们能够研究规范理论现象如何转化为没有显式规范对称的耦合自由度系统以及规范对称如何出现的基本问题。WP3允许我们研究约束-定义转变的静力学，更重要的是它的动力学，与热化的存在和不存在的关系，许多体定位和量子疤痕的动力学作用。虽然实验工作将集中在阿贝尔lgt上，但理论将设计以及非阿贝尔对称性的可扩展实现。在《DYNAMITE》中，实验和理论将不可分割地纠缠在一起。其结果将提供对量子多体物理前沿突出现象的前所未有的控制。

As of today, Quantum Simulators (QS) are the systems that can address, deepen our understanding of, and ultimately solve some of the most challenging problems of contemporary science: from quantum many body dynamics, through static and transient high Tc superconductivity, to the design of new materials. In DYNAMITE, we will design, realize in the labs, and characterize a new generation of QS with ultracold atoms and beyond. With ascending degree of experimental complexity this involves: (WP1) systems with statistical gauge fields, i.e. “single-component” lattice or continuum systems with density-dependent gauge fields changing the effective quantum statistics of the particles and realizing topological gauge theories; (WP2) systems in dynamical lattices, with “matter” living on the sites, and additional dynamical fields/particles living on the bonds; (WP3) lattice gauge theory models (LGT), from systems with Abelian (Z2, U(1)) to non-Abelian local gauge symmetry. Such systems address questions from condensed matter physics, nuclear physics, high energy physics, and material science: In particular, WP1 allows one to engineer topological gauge theories in the continuum, and to design and control novel types of topological and chiral order, with possible applications to quantum computing and quantum memories. The theoretical and experimental goal here is to tailor the proper matter dependence for the gauge fields, which corresponds to correctly imposing the local symmetry constraint of the gauge theory. WP2 allows one to design and study the interplay between topological order and symmetry breaking. Simpler systems without gauge invariance that are already simulated in the labs, permit us indeed to study the fundamental question of how gauge theory phenomena translate into systems of coupled degrees of freedom without explicit gauge symmetry and how gauge symmetry can emerge. WP3 allows us to study statics of the confinement-deconfinement transition, and more importantly its dynamics, relation to absence/presence of thermalization, the dynamical role of many body localization and quantum scars. While experimental work will focus on Abelian LGTs, theory will design as well scalable implementations of non-Abelian symmetries. In DYNAMITE, experiment and theory will be inseparably entangled. Its results will provide unprecedented control over salient phenomena at the frontier of quantum many-body physics.