The critical interaction strength of normal-to-MQST transition for dressed states. The red diamonds and black circles indicate the critical interaction strength of phase transition versus the coupling strength Ω, which are obtained from the CGPEs [Eq. (5)] and the decoupled equations [Eq. (7)], respectively. The purple line is the analytical result [Eq. (18)] calculated from the three-mode equation [Eq. (14)]. Other parameters: atom number N = 10000, spatial separation x0 = 3.