Analysing Polariton States in the Non-Dispersive regime of cQED

Strongly driven qubit-resonator systems have recently gained attention as they can be used to generate polariton states. These are hybrid states obtained by dressing a coupled qubit-resonator system with a drive and can be of great utility in realizing phenomena such as electromagnetically induced transparency. Previous theoretical and experimental studies have almost exclusively limited themselves to the dispersive regime, where the qubit-resonator detuning is much greater than their coupling. In this work, we theoretically study a driven transmon -resonator system outside the dispersive regime. We analyze this system using two approaches that give complementary insights: eigenmode analysis and master equation simulations. We show how the non-dispersive coupling of the higher levels of the qubit-resonator system modifies the polariton eigenstates and the corresponding transition frequencies. Furthermore, we compare our predictions to experimental data from a lumped resonator-transmon system operating outside the dispersive regime and find excellent agreement between theory and experiment.