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Theoretical and Mathematical Physics

Resonances and Tunneling in the Tight-Binding Approximation to Scattering in a Quantum Billiard

A. A. Arseniev

Published Oct 1, 2004• 1 citation
Publisher
DOI
10.1023/b:tamp.0000043857.79577.c4

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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.