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

Spin glasses are quintessential examples of complex matter. Although their ordering lacks complete theoretical understanding, abstract models of spin glasses inform problems in other fields, such as combinatorial optimization and artificial intelligence—where they form a mathematical basis for neural network computing. We demonstrate the ability to realize a spin glass of a distinct 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, and climate change; this work shows it to be directly observable in a physically realized system.