  Atoms and ions confined with electric and optical fields form the basis of
many current quantum simulation and computing platforms. When excited to
high-lying Rydberg states, long-ranged dipole interactions emerge which
strongly couple the electronic and vibrational degrees of freedom through
state-dependent forces. This vibronic coupling and the ensuing hybridization of
internal and external degrees of freedom manifest through clear signatures in
the many-body spectrum. We illustrate this by considering the case of two
trapped Rydberg ions, for which the interaction between the relative vibrations
and Rydberg states realizes a quantum Rabi model. We proceed to demonstrate
that the aforementioned hybridization can be probed by radio frequency
spectroscopy and discuss observable spectral signatures at finite temperatures
and for larger ion crystals.
