Directly observing replica symmetry breaking in a vector quantum-optical spin glass

Abstract: Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals with impurities, and artificial intelligence -- where they form a mathematical basis for neural network computing and brain modeling. We demonstrate the ability of an active quantum gas microscope to realize a spin glass of a novel driven-dissipative and vector form. By microscopically visualizing its glassy spin states, the technique allows us to directly measure replica symmetry breaking and the resulting ultrametric hierarchical structure. Ultrametricity is known to be emergent in models of evolution, protein folding, climate change, and infinite-range equilibrium spin glasses; this work shows it to be directly observable in a physically realized system.