Resonator mediated controlling single photon transport in one-dimensional waveguide coupling to a giant atom

We theoretically investigate coherent controlling single photon transport in one-dimensional waveguide coupled to a giant atom interacting with a resonator. The giant atom is considered as a Alpha-type system. One transition of the atom couples to the waveguide and the other one is driven by the resonator. Single photon scattering amplitudes are calculated for three kinds of coupling schematics, respectively. Both the analytical and numerical results show that single photon scattering properties can be manipulated by adjusting the size of the giant atom, the coupling strengths of the waveguide-resonator and resonator-giant atom. Specifically, the transmission spectra exhibit two Rabi-splitting dips and the locations of the dips are strongly dependent on the size of the giant atom (GA). It also shows that the resonant single photon can be tuned from being transmitted to being reflected by controlling the coupling strength. Our results may find applications in designing quantum devices based on giant atom at single -photon level.