Exciton Transport Coherent with Upper and Lower Polaritons

In the strong exciton-cavity coupling regime, exciton polaritons play a pivotal role in governing exciton transport. However, the specific contributions of the two branches of polaritons to exciton current remain unexplored. Here, we decompose the exciton current operator into components coherent with the upper and lower polaritons. Subsequently, we employ the quantum master equation to investigate the exciton current coherent with these two polariton branches. Our findings reveal that in the blue detuning regime, where the optical frequency exceeds the molecular excitation energy, the contribution of the exciton current coherent with the lower polariton is more pronounced. Conversely, in the red detuning regime, where the optical frequency is lower than the molecular excitation energy, the contribution of the exciton current coherent with the upper polariton prevails. We elucidate two critical factors influencing these contributions: firstly, the ratio of excitons to photons in the polariton branches. Due to the smaller decay rate of molecules compared to that of the cavity, the polariton branch with a higher proportion of excitons contributes more to coherent exciton current. Secondly, the energy gap between the polariton branch and the dark states; a smaller energy difference in a branch provides a larger contribution to coherent exciton current.