  We study the dynamic sensitivity of the quantum Rabi model, which exhibits
quantum criticality in the finite-component-system case. This dynamic
sensitivity can be detected by introducing an auxiliary two-level atom
far-off-resonantly coupled to the cavity field of the quantum Rabi model. We
find that when the quantum Rabi model goes through the critical point, the
auxiliary atom experiences a sudden decoherence, which can be characterised by
a sharp decay of the Loschmidt echo. Our scheme will provide a reliable way to
observe quantum phase transition in ultrastrongly coupled quantum systems.
