  We investigate signatures of chaos and equilibration in the quantum Rabi
model, which exhibits a quantum phase transition when the ratio of the atomic
level-splitting to bosonic frequency grows to infinity. We show that
out-of-time-order correlator derived from the Loschmidt echo signal quickly
saturates in the normal phase and reveals exponential growth in the
superradiant phase which is associated with the onset of quantum chaos.
Furthermore, we show that the effective time-averaged dimension of the quantum
Rabi system can be large compared to the spin system size which leads to
suppression of the temporal fluctuations and equilibration of the spin system.
