Atomic Gauge and Entanglement Theories

ended

AGEnTh is an interdisciplinary proposal which aims at theoretically investigating atomic many-body systems (cold atoms and trapped ions) in close connection to concepts from quantum information, condensed matter, and high energy physics. The main goals of this programme are to: I) find to scalable schemes for the measurements of entanglement properties, and in particular entanglement spectra, by proposing a shifting paradigm to access entanglement focused on entanglement Hamiltonians and field theories instead of probing density matrices; II) show how atomic gauge theories (including dynamical gauge fields) are ideal candidates for the realization of long-sought, highly-entangled states of matter, in particular topological superconductors supporting parafermion edge modes, and novel classes of quantum spin liquids emerging from clustering; III) develop new implementation strategies for the realization of gauge symmetries of paramount importance, such as discrete and SU(N)xSU(2)xU(1) groups, and establish a theoretical framework for the understanding of atomic physics experiments within the light-from-chaos scenario pioneered in particle physics. These objectives are at the cutting-edge of fundamental science, and represent a coherent effort aimed at underpinning unprecedented regimes of strongly interacting quantum matter by addressing the basic aspects of probing, many-body physics, and implementations. The results are expected to (i) build up and establish qualitatively new synergies between the aforementioned communities, and (ii) stimulate an intense theoretical and experimental activity focused on both entanglement and atomic gauge theories. In order to achieve those, AGEnTh builds: (1) on my background working at the interface between atomic physics and quantum optics from one side, and many-body theory on the other, and (2) on exploratory studies which I carried out to mitigate the conceptual risks associated with its high-risk/high-gain goals.