Probing dressed states and quantum nonlinearities in a strongly coupled three-qubit waveguide system under optical pumping

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.