PT restoration via increased loss and gain in the-symmetric Aubry-Andr\'{e} model

In systems with ``balanced loss and gain,'' the~\textit{PT}~symmetry is broken by increasing the non-Hermiticity or the loss-gain strength. We show that finite lattices with oscillatory,~\textit{PT} -symmetric potentials exhibit unexpected~\textit{PT} -symmetry breaking and restoration. We obtain the~\textit{PT}~phase diagram as a function of potential periodicity, which also controls the location complex eigenvalues in the lattice spectrum. We show that the sum of~\textit{PT}~potentials with nearby periodicities leads to~\textit{PT} -symmetry restoration, where the system goes from a \textit{PT} -broken state to a~\textit{PT} -symmetric state as the average loss-gain strength is increased. We discuss the implications of this transition for the propagation of a light in an array of coupled waveguides. Reference [1] C. H. Liang, D. D. Scott, and Y. N. Joglekar, Phys. Rev. A \textbf{89}, 030102 (2014).