  We propose a hybrid quantum model combining cavity QED and optomechanics,
which allows the occurrence of equilibrium superradiant quantum phase
transition (QPT) triggered by a single photon. This single-photon-triggered QPT
exists both in the cases of ignoring and including the so-called $A^2$ term,
i.e., it is immune to the no-go theorem. It originally comes from the
photon-dependent quantum criticality featured by the proposed hybrid quantum
model. Moreover, a reversed superradiant QPT is induced by the competition
between the introduced $A^2$ term and the optomechanical interaction. This work
offers an approach to manipulate QPT with a single photon, which should inspire
the exploration of single-photon quantum-criticality physics and the
engineering of new single-photon quantum devices.
