PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold

Eva-Maria Graefe, H. F. Jones

The $PT$ symmetric potential $V_0[\cos (2\pi x/a)+i\lambda \sin (2\pi x/a)]$ has a completely real spectrum for $\lambda \le 1$, and begins to develop complex eigenvalues for $\lambda >1$. At the symmetry-brea…