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We study a three-qubit waveguide system in the presence of optical pumping,when the side qubits act as atomlike mirrors, manifesting in a stronglight-matter coupling regime. The qubits are modelled as Fermionic two-levelsystems, where we account for important saturation effects and quantumnonlinearities. Optically pumping this system is shown to lead to a richmanifold of dressed states that can be seen in the emitted spectrum, and weshow two different theoretical solutions using a medium-dependent masterequation model in the Markovian limit, as well as using matrix product stateswithout invoking any Markov approximations. We demonstrate how a rich nonlinearspectrum is obtained by varying the relative decay rates of the mirror qubitsas well as their spatial separation, and show the limitations of using aMarkovian master equation. Our model allows one to directly model giant-atomphenomena, including important retardation effects and multi-photonnonlinearities. We also show how the excited three qubit system, in a strongcoupling regime, deviates significantly from a Jaynes-Cummings model whenentering the nonlinear regime.

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