  In this paper, we study the synchronization of qubits induced by the
dynamical Casimir effect in an atom-cavity quantum electrodynamics system. Our
investigation revolves around a pragmatic configuration of a quantum system,
where two superconducting qubits are coupled to a shared coplanar waveguide
resonator terminated at one end by a superconducting quantum interference
device. The theoretical analyses of the system dynamics reveal sufficient
conditions for ensuring synchronization which are anticipated to be
accomplished by photon generation in the resonator. By numerically analyzing
the time evolution of the system, we confirm that the conditions are satisfied
by photon generation via the dynamical Casimir effect, resulting in qubit
synchronization. Notably, we unveil a remarkable feature that is unique to
synchronization induced by the dynamical Casimir effect: the differences in the
initial states of qubits and the differences in the coupling strengths of
qubits to an electromagnetic field affect the synchronization independently
without overlap between these factors.
