  We observe the nonlinearity of the Jaynes-Cummings (JC) ladder in the
Autler-Townes spectroscopy of the hyperfine ground states for a Rydberg-dressed
two-atom system. Here the role of the two-level system in the JC model is
played by the presence or absence of a collective Rydberg excitation, and the
bosonic mode manifests as the number $n$ of single atom spin flips,
symmetrically distributed between the atoms. We measure the normal-mode
splitting and $\sqrt{n}$ nonlinearity as a function of detuning and Rabi
frequency, thereby experimentally establishing the isomorphism with the JC
model.
