Quantum synchronization and controllable Einstein-Podolsky-Rosen steering of a dynamical Casimir waveguide system composed of giant atoms

We obtain the quantum synchronization and controllable Einstein-Podolsky-Rosen (EPR) steering through theoretical research in a Dynamical Casimir array (DCA) composed of two giant atoms. We achieve one-way or two-way EPR steering between giant atoms, as well as the reversal and exchange of monogamy relations by adjusting system parameters. Remarkably, we find that the system temperature can serve as a switch for regulating different types of EPR steering. By adjusting this switch, we obtain the sudden death of EPR steering between giant atoms and the resurrection of two-way EPR steering between Casimir photons and giant atoms. Most importantly, the resurrection of EPR steering generated by the temperature shows the synchronicity and shareability of multipartite EPR steering. Contrary to the monogamy relations, the shareability of EPR steering allows the state of one party to be steered by two or more observers. The emergence of quantum synchronization and shareability of EPR steering provides an innovative perspective and approach for studying multipartite EPR steering and has potential applications in many quantum information protocols. •The manuscript investigates the quantum synchronization and controllable EPR steering in a dynamic Casimir array.•The work innovatively obtains the synchronicity and shareability of EPR steering by adjusting the temperature.•Temperature causes the sudden death and resurrection of the EPR steering between Casimir photons and giant atoms.•Adjusting the system parameters achieves the reversal and exchange of monogamy relations in EPR steering.•The work provides an innovative approach and has potential applications in many quantum information protocols.