  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.
