Decoding transverse spin dynamics by energy-resolved correlation measurement

We study transverse spin dynamics on a microscopic level by measuring energy-resolved spin correlations in a weakly-interacting Fermi gas. The trapped cloud behaves as a many-body spin-lattice in energy space with effective long-range interactions, simulating a collective Heisenberg model. We observe the flow of correlations in energy space in this quasi-continuous system, revealing the connection between the evolution of the magnetization and the localization or spread of correlations. This work highlights energy-space correlation as a new observable in quantum phase transition studies, decoding system features that are hidden in macroscopic measurements.Comment: 15 pages, 8 figure