  We demonstrate that the quantum phase transition (QPT) of the Rabi model and
critical dynamics near the QPT can be probed in the setup of a single trapped
ion. We first show that there exists equilibrium and non-equilibrium universal
functions of the Rabi model by finding a proper rescaling of the system
parameters and observables. We then propose a scheme that can faithfully
realize the Rabi model in the limit of a large ratio of the effective atomic
transition frequency to the oscillator frequency using a single trapped-ion and
therefore the QPT. It is demonstrated that the predicted universal functions
can indeed be observed based on our scheme. Finally, the effects of realistic
noise sources on probing the universal functions in experiments are examined.
