  Phase synchronization refers to a kind of collective phenomenon that the
phase difference between two or more systems is locked, and it has widely been
investigated between systems with the identical physical properties, such as
the synchronization between mechanical oscillators and the synchronization
between atomic ensembles. Here, we investigate the synchronization behavior
between the mechanical oscillator and the atomic ensemble, the systems with
different physical properties, and observe a novel synchronization phenomenon,
i.e., the phase sum, instead of phase difference, is locked. We refer to this
distinct synchronization as the phase anti-synchronization, and show that the
phase anti-synchronization can be achieved in both the classical and quantum
level, which means this novel collective behavior can be tested in experiment.
Also, some interesting connections between phase anti-synchronization and
quantum correlation is found.
