Energy-resolved spin correlation measurements: Decoding transverse spin dynamics in weakly interacting Fermi gases

We study transverse spin dynamics on a microscopic level by measuring energy-resolved spin correlations in weakly interacting Fermi gases (WIFGs). 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 of WIFGs, decoding system features that are hidden in macroscopic measurements.