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

今天，量子模拟器(QS)是能够解决、加深我们对当代科学中一些最具挑战性的问题的理解并最终解决这些问题的系统：从量子多体动力学，到静态和瞬时高T_c超导，再到新材料的设计。在炸药中，我们将设计、在实验室中实现并表征具有超冷原子和更远的新一代QS。随着实验复杂性的增加，这涉及到：(WP1)具有统计规范场的系统，即具有依赖密度的规范场的“单分量”晶格或连续系统，它改变了粒子的有效量子统计并实现了拓扑规范理论；(WP2)动力学晶格中的系统，“物质”住在格点上，附加的动力场/粒子住在键上；(WP3)格点规范理论模型(LGT)，从具有阿贝尔(Z2，U(1))对称性的系统到非阿贝尔局域规范对称性的系统。这些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：尤其是，WP1允许人们在连续统中设计拓扑规范理论，并设计和控制新型的拓扑和手征有序，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定制适当的物质依赖关系，这对应于正确地施加规范理论的局域对称性约束。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。已经在实验室中模拟的没有规范不变性的更简单的系统，确实允许我们研究基本问题，即规范理论现象如何转化为没有显式规范对称性的耦合自由度系统，以及规范对称性如何出现。WP3使我们能够研究禁闭-解禁闭转变的静力学，更重要的是它的动力学，与热化的缺失/存在的关系，多体局域化和量子伤痕的动力学作用。虽然实验工作将集中在阿贝尔LGT上，但理论将设计非阿贝尔对称的可伸缩实现。在炸药中，实验和理论将密不可分。它的结果将对量子多体物理前沿的显著现象提供前所未有的控制。

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.