Non-Markovianity of an Atom in a Semi-Infinite Rectangular Waveguide


 We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM$_{mn}$) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity $\mathcal{N}_{1}$ can be found as the atom-mirror distance is large enough, however, the asymptotic value of $\mathcal{N}_{2}$ of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that $\mathcal{N}_{1}$ is a constant, and the analytical expression for $\mathcal{N}_{2}$ is related to the parameters associated with the modes, which is related to the interference of the two modes.