It is known that when two identical waves are injected from left and right on a complex PT-symmetric scattering potential the two-port s-matrix can have uni-modular eigenvalues. If this happens for all energies, there occurs a perfect emission of waves at both ends. We call this phenomenon transparency. Using the versatile PT-Symmetric complex Scarf II potential, we demonstrate analytically that the transparency occurs when the potential has real discrete spectrum i.e., when PT-symmetry is exact(unbroken). Next, we find that exactness of PT-symmetry is only sufficient but not necessary for the transparency. Two other PT-symmetric domains of Scarf II reveal transparency without the PT-symmetry being exact. In these two cases there exist only scattering states. In one case the real part of the potential is a well devoid of real discrete spectrum and in the other real part is a barrier. Other numerically solved models also support our findings.

http://arxiv.org/abs/1410.5530
Quantum Physics (quant-ph)