  We study a three-qubit waveguide system in the presence of optical pumping,
when the side qubits act as atomlike mirrors, manifesting in a strong
light-matter coupling regime. The qubits are modelled as Fermionic two-level
systems, where we account for important saturation effects and quantum
nonlinearities. Optically pumping this system is shown to lead to a rich
manifold of dressed states that can be seen in the emitted spectrum, and we
show two different theoretical solutions using a medium-dependent master
equation model in the Markovian limit, as well as using matrix product states
without invoking any Markov approximations. We demonstrate how a rich nonlinear
spectrum is obtained by varying the relative decay rates of the mirror qubits
as well as their spatial separation, and show the limitations of using a
Markovian master equation. Our model allows one to directly model giant-atom
phenomena, including important retardation effects and multi-photon
nonlinearities. We also show how the excited three qubit system, in a strong
coupling regime, deviates significantly from a Jaynes-Cummings model when
entering the nonlinear regime.
