  While non-Hermitian systems are normally constructed through incoherent
coupling to a larger environment, recent works have shown that under certain
conditions coherent couplings can be used to similar effect. We show that this
new paradigm enables the behavior associated with the PT- symmetric phase of a
non-Hermitian subsystem to control the containing Hermitian system through the
coherent couplings. This is achieved in parametric nonlinear wave mixing where
simultaneous second harmonic generation replaces the role of loss to induce
non-Hermitian behavior that persists through a full exchange of power within
the Hermitian system. These findings suggest a new approach for the engineering
of dynamics where energy recovery and sustainability are of importance that
could be of significance for photonics and laser science.
