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ALT Figure showing the differential phase sensing protocol in three parts. The top schematic shows how the atoms in ensembles are initially in their excited ground states, shown by globes with colorful areas on one of the poles. An entangler is applied, causing each to acquire a distinct phase, shown by horizontal arrows on the globes. Then a joint measurement estimates the differential phase for each. The second schematic shows the target state after the entangling process, which is an entangled Lieb-Mattis state. The last part of the figure shows the Wigner distributions represented by globes with colorful areas and alternating signs of all Dicke-state combinations.






















