  Non-Hermitian Hamiltonians play an important role in many branches of
physics, from quantum mechanics to acoustics. In particular, the realization of
PT, and more recently -- anti-PT symmetries in optical systems has proved to be
of great value from both the fundamental as well as the practical perspectives.
Here, we study theoretically and demonstrate experimentally a novel anyonic-PT
symmetry in a coupled lasers system. This is achieved using complex coupling --
of mixed dispersive and dissipative nature, which allows unprecedented control
on the location in parameter space where the symmetry and symmetry-breaking
occur. Moreover, our method allows us to realize the more familiar special
cases of PT and anti-PT symmetries using the same physical system. In a more
general perspective, we present and experimentally validate a new relation
between laser synchronization and the symmetry of the underlying non-Hermitian
Hamiltonian.
