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

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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.