We developed a discrete coordinate scattering approach to analyze the coherent transport of a single photon in a nano-structures. We take an example as photons propagate in a one-dimensional coupled-resonator waveguide and is scattered by a controllable two-level system located inside one of the resonators of this waveguide. Our approach, which uses discrete coordinate representation, unifies low and high energy effective theories for single-photon scattering. We show that the controllable two-level system can behave as a quantum switch for the coherent transport of a single photon. This study may inspire new electro-optical single-photon quantum devices. We also suggest an experimental setup based on superconducting transmission line resonators and qubits.

Motivated by the above investigations for conceptual quantum device, we propose a general approach to actively control the coupling between a qubit and its surrounding system based on the dynamic Zeno effect. To enable this quantum control scheme, the energy level spacing of the qubit is periodically modulated at a high frequency so that the interaction can be turned -on and -off when controlling the ratios of the modulating amplitude to this frequency. This study inspires a conceptual design of a quantum switch based on the quantum Zeno effect, which controls the coherent transport of single photons along a one-dimensional waveguide. The reflection rate is analytically calculated and its vanishing in the above mentioned ratios shows the quantum Zeno effect happening on its coupled qubit. The exact solutions of the Floquet theory based on numerical analysis well confirms our theoretical prediction.

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