We study the scattering properties of N identical one-dimensional localized PT -symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum scatterers, and apply that theory to demonstrate that the spectral singularities and PT -symmetric transitions of single scattering cells may be observed in coupled systems, at the same or distinct values of the critical parameters, depending on the connection modes under which the scattering objects are coupled. We analyse the influences of the connection configuration on the related transport properties such as spectral singularities and anisotropic transmission resonances.
Employing tight-binding approximation we derive a transfer matrix formalism for one-dimensional single photon transport through a composite scattering center, which consists of parallel connected resonator optical waveguides. By solving the single-mode eigenvectors of the Hamiltonian, we investigate the quantum interference effects of parallel couplings on the photon transport through this parallel waveguide structure. We find a perfect reflection regime determined by the number of coupled resonator waveguides. Numerical analysis reveals that by changing atom transition frequency, the window of perfect reflection may shift to cover almost all incoming photon energy, indicating the effective control of single photon scattering by photon-atom interaction.
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