  Quantum criticality usually occurs in many-body systems. Recently it was
shown that the quantum Rabi model, which describes a two-level atom coupled to
a single model cavity field, presents quantum phase transitions from a normal
phase to a superradiate phase when the ratio between the frequency of the two
level atom and the frequency of the cavity field extends to infinity. In this
work, we study quantum phase transitions in the quantum Rabi model from the
fidelity susceptibility perspective. We found that the fidelity susceptibility
and the generalized adiabatic susceptibility present universal finite size
scaling behaviors near the quantum critical point of the Rabi model if the
ratio between frequency of the two level atom and frequency of the cavity field
is finite. From the finite size scaling analysis of the fidelity
susceptibility, we found that the adiabatic dimension of the fidelity
susceptibility and the generalized adiabatic susceptibility of fourth order in
the Rabi model are $4/3$ and $2$, respectively. Meanwhile the correlation
length critical exponent and the dynamical critical exponent in the quantum
critical point of the Rabi model are found to be $3/2$ and $1/3$ respectively.
Since the fidelity susceptibility and the generalized adiabatic susceptibility
are the moments of the quantum noise spectrum which is directly measurable by
experiments in linear response regime, the scaling behavior of the fidelity
susceptibility in the Rabi model could be tested experimentally. The simple
structure of the quantum Rabi model paves the way for experimentally observing
the universal scaling behavior of the fidelity susceptibility at a quantum
phase transition.
