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The purpose of this paper is to study the dynamics of a coherent feedbacknetwork where two two-level atoms are coupled with a semi-infinite waveguide.In this set-up, the two-level atoms can work as the photon source, and thephotons can be emitted into the waveguide via the nonchiral or chiral couplingsbetween the atom and the waveguide, according to whether the coupling strengthsbetween the atoms and different directional propagating modes in the waveguideare identical or not. For the photon emitted by one of the two atoms, it can bereflected by the terminal mirror, or interact with the other atom, and then thephoton can re-interact with the former atom. When the two atoms are bothinitially excited, finally there can be two-photon, one-photon or zero-photonstates in the waveguide via the spontaneous emission and feedback interactions,and this is influenced by the locations of the atoms and the chirality of thecoupling between the atom and the waveguide. Similarly, if only one of the twoatoms is initially excited, there can be zero or one photon in the waveguide.Thus we can control the number of the photons in the waveguide and the atomicstates by tuning the feedback loop length and the chiral couplings between theatom and waveguide. The photonic state in the waveguide is analyzed in thefrequency domain and the spatial domain, and the transient process of photonemissions can be better understood based on the comprehensive analysis in thesetwo domains.

Quantum feedback control of a two-atom network closed by a semi-infinite waveguide