Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits

A recent theoretical analysis [A. Blais , Phys. Rev. A 69, 062320 (2004)] and experimental results [A. Wallraff , Nature (London) 431, 162 (2004)] show that interesting transport properties of a single microwave photon emerge when a quantum bit in a cavity is coupled to a one-dimensional waveguide. Here we adopt a real-space model Hamiltonian to give a unified approach which accounts for the experimental results, and make new predictions on the properties of single photon transport, such as the general Fano line shape, symmetric vacuum Rabi splitting for a leaky cavity at resonance, and a one-photon switching capability.