  As the simplest and most fundamental model describing the interaction between
light and matter, a breakdown in the rotating wave approximation of the Rabi
model leads to phase transition versus coupling strength when the frequency of
the qubit greatly surpasses that of the oscillator. Besides the phase
transition revealed in the ground state, we show that the dynamics of physical
quantities can reflect such a phase transition for this model. In addition to
the excitation of the bosonic field in the ground state, we show that the
witness of inseparability (entanglement), mutual information, quantum Fisher
information, and the variance of cavity quadrature can be employed to detect
the phase transition in quench. We also reveal the negative impact of
temperature on checking the phase transition by quench. This model can be
implemented using trapped ions, superconducting artificial atoms coupled
bosonic modes, and quantum simulations. By reflecting the phase transition in a
fundamental quantum optics model without imposing the thermodynamic limit, this
work offers an idea to explore phase transitions by non-equilibrium process for
open quantum systems.
