“…1(c) and 1(d) show the dressed-state splitting 1, as a function of Stark shift 0 for weak (Ω/ = 0.01) and strong (Ω/ = 2.1) control fields by fixing / = 4, respectively, where = ±1, 0 represents the upper, lower, and middle helicity branches, respectively. An asymmetry structure of the dressed-state splitting between the red and blue light-cavity detuning is observed, where the result is analogous to our recent study on the Stark shift mediated Jaynes-Cummings model [37]. Moreover, the 0 -dependent lower branch splitting 1,− is significantly enhanced with the increasing negative | 0 |, while gradually saturated to a constant for positive 0 , vice verse for the case of the higher branch splitting 1,+ .…”