Quantum mechanical treatment of two-level atoms coupled to continuum with an ultraviolet cutoff

In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We propose a novel single frequency sampling method utilizing a UV-cutoff that allows us to treat the singularities in real space scattering potential despite the non-convergence property. We also study the conditions under which the linearization of the coupling coefficient is an accurate assumption and find the resulting spontaneous emission and transport characteristics taking the radiative and non-radiative decay rates into account. This allows us to confirm and expand on the findings of the existing literature while obtaining the dynamic electronic polarizability for the two-level atom confined to a 1D waveguide while using an interaction Hamiltonian with rotating-wave approximation.