Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity

We theoretically demonstrate the influence of dark and bright states on vacuum Rabi splitting (VRS) and optical bistability (OB) of the multi-wave-mixing (MWM) process in a collective four-level atomic-cavity coupling system. We numerically investigate the multidressed VRS and OB behavior of the zero- and high-order transmitted cavity modes of MWM signals. A further study demonstrates that VRS and self-Kerr nonlinearity OB can coexist and compete with each other in a cascade relationship, based on which we achieve the goal to control VRS and OB simultaneously through the dark state in the atomic system.